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Author: JSFHYuri Zlatsin 10-Oct-2011 Audit: Omer Yagel 104131 - Madar H Home Assignment #3 and #4 spring 2011
<Text-field style="Heading 1" layout="Heading 1">Question 1</Text-field> Given 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 A. Show that 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 is a solution to the equation. B. Find solutions for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiMUYnL0YzUSdub3JtYWxGJ0Y+Rj4tSSNtb0dGJDYtUSI9RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZVLUY7NiRRIjBGJ0Y+Rj4= ,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.
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field> 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 print(); # input placeholder JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwmKiYsJkYnIiIiRitGKyEiIkkkX0MxR0YlRitGKyooRiciIiRGKkYsSSRfQzJHRiVGK0Yr And the solution with the initial conditions: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwmKiQsJkYnIiIiRitGKyEiIkYsKiZGJyIiJEYqRixGKw==
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Answer for A</Font></Text-field> We show that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EnYHlfXzFgRictSSNtb0dGJDYtUSomY29sb25lcTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjRRJ2l0YWxpY0YnLUYwNi1RKCZzcmFycjtGJ0YzRjZGOUY7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklGVi1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRidGMy1GIzYlRkotRjA2LVEiK0YnRjNGNkY5RjtGPUY/RkFGQy9GRlEsMC4yMjIyMjIyZW1GJy9GSUZfb0Zlbi8lLmxpbmV0aGlja25lc3NHRmhuLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmVvLyUpYmV2ZWxsZWRHRjgtRjA2LVEiOkYnRjNGNkY5RjtGPUY/RkFGQ0ZFRkg= is a solution: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHlfXzFgRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y7USdub3JtYWxGJw== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder KiQsJkkieEc2IiIiIkYmRiYhIiI= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EnYHlfXzFgRictSSNtb0dGJDYtUSInRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHUSYwLjBlbUYnLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y0USdpdGFsaWNGJ0Yz LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LCQqJCwmSSJ4RzYiIiIiRidGJyEiIyEiIg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHlfXzFgRictSSNtb0dGJDYtUSInRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHUSYwLjBlbUYnRi8tSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjRRJ2l0YWxpY0YnRjM= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LCQqJCwmSSJ4RzYiIiIiRidGJyEiJCIiIw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Now we compare it to the original equation: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElc3Vic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYpLUYsNiVRInlGJ0YvRjItRjY2JC1GIzYjLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiPUYnRkQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkwvJSlzdHJldGNoeUdGTC8lKnN5bW1ldHJpY0dGTC8lKGxhcmdlb3BHRkwvJS5tb3ZhYmxlbGltaXRzR0ZMLyUnYWNjZW50R0ZMLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGZW4tRiw2I1EnYHlfXzFgRidGPS1GRzYtUSIsRidGREZKL0ZORjFGT0ZRRlNGVUZXL0ZaUSYwLjBlbUYnL0ZnblEsMC4zMzMzMzMzZW1GJy1GLDYlUSRPREVGJ0YvRjJGRC1GLDYjUSFGJw== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvLCgqKEkieEdGKCIiIiwmRi9GMEYwRjBGMC1JJWRpZmZHRiY2JCokRjEhIiItSSIkR0YmNiRGLyIiI0YwRjAtRjM2JEY1Ri8hIiNGNUY9IiIhNyMvLCgqKEYvRjBGMUYwLUYzNiRGO0YvRjBGMEY7Rj1GNUY9Rj4= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LywoKiZJInhHNiIiIiIsJkYlRidGJ0YnISIjIiIjKiRGKEYpRioqJEYoISIiRikiIiE= JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEpc2ltcGxpZnlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYjUSFGJy1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUWVwLywoKiZJInhHNiIiIiIsJkkieEc2IiIiIiIiIiIiIiEiIyIiIyokLCZJInhHNiIiIiIiIiIiIiIhIiMiIiMqJCwmSSJ4RzYiIiIiIiIiIiIiISIiISIjIiIhRicvJSthY3Rpb250eXBlR1E7bWFwbGVzb2Z0LmNvbTpsYWJlbChMMzQ4MylGJy8lJXZpZXdHUSZsYWJlbEYnRjovRjNRJ25vcm1hbEYn LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LyIiIUYj JSFH
JSFH
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Answer for B</Font></Text-field> We find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EnYHlfXzJgRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y7USdub3JtYWxGJ0Y9Rj0=: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder KiYtSSJ2RzYiNiNJInhHRiUiIiIsJkYnRihGKEYoISIi LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EnYHlfXzJgRictSSNtb0dGJDYtUSInRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHUSYwLjBlbUYnLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y0USdpdGFsaWNGJ0Yz LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJiomLUklZGlmZkdGJjYkLUkidkdGKDYjSSJ4R0YoRjQiIiIsJkY0RjVGNUY1ISIiRjUqJkYxRjVGNiEiI0Y3Ris= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvLCgqJi1JJWRpZmZHRiY2JC1JInZHRig2I0kieEdGKC1JIiRHRiY2JEY1IiIjIiIiLCZGNUY6RjpGOiEiIkY6KiYtRjA2JEYyRjVGOkY7ISIjRkAqJkYyRjpGOyEiJEY5IiIhNyMvLCgqJi1GMDYkRj5GNUY6RjtGPEY6Rj1GQEZBRjlGQw== We get: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvLCgqKEkieEdGKCIiIiwmRi9GMEYwRjBGMC1JJWRpZmZHRiY2JComLUkidkdGKDYjRi9GMEYxISIiLUkiJEdGJjYkRi8iIiNGMEYwLUYzNiRGNUYvISIjRjVGQCIiITcjLywoKihGL0YwRjFGMC1GMzYkRj5GL0YwRjBGPkZARjVGQEZB 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvLCYqJi1JJWRpZmZHRiY2JC1JInZHRig2I0kieEdGKC1JIiRHRiY2JEY1IiIjIiIiRjVGOkY6LUYwNiRGMkY1ISIjIiIhNyMvLCYqJi1GMDYkRjtGNUY6RjVGOkY6RjtGPUY+ 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvLCYqJi1JJWRpZmZHRiY2JC1JInVHRig2I0kieEdGKEY1IiIiRjVGNkY2RjIhIiMiIiFGKw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnZHNvbHZlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1FfcC8sJiomLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHNiI2I0kieEc2IkkieEc2IiIiIkkieEc2IiIiIiIiIi1JInVHNiI2I0kieEc2IiEiIyIiIUYnLyUrYWN0aW9udHlwZUdRO21hcGxlc29mdC5jb206bGFiZWwoTDM1MjEpRicvJSV2aWV3R1EmbGFiZWxGJ0Y6L0YzUSdub3JtYWxGJw== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInVHNiI2I0kieEdGJSomSSRfQzFHRiUiIiJGJyIiIw== 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvLUklZGlmZkdGJjYkLUkidkdGKDYjSSJ4R0YoRjMqJkkkX0MxR0YoIiIiRjMiIiNGKw== Integrating both sides: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbW9HRiQ2LVErJkludGVncmFsO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R1EldHJ1ZUYnLyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZELUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR0Y5L0YwUSdpdGFsaWNGJy1GLDYtUSInRidGL0YyRjUvRjhGNEY6L0Y9RjRGPkZAL0ZDUSwwLjExMTExMTFlbUYnRkUtRiw2LVEwJkRpZmZlcmVudGlhbEQ7RidGL0YyRjVGUkY6RlNGPkZARkJGRS1GSDYlUSJ4RidGS0ZNLUYsNi1RIj1GJ0YvRjJGNUZSRjpGU0Y+RkAvRkNRLDAuMjc3Nzc3OGVtRicvRkZGam4tRiw2LVEmJmludDtGJ0YvRjJGNUY3RjpGPEY+RkBGQkZFLUZINiVRJHJoc0YnL0ZMRjRGLy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUZINiNRIUYnLUkobWFjdGlvbkdGJDYlLUkqbXZlcmJhdGltR0YkNiNRXW8vLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInZHNiI2I0kieEc2IkkieEc2IiomSSRfQzFHNiIiIiJJInhHNiIiIiNGJy8lK2FjdGlvbnR5cGVHUTttYXBsZXNvZnQuY29tOmxhYmVsKEwzNTIzKUYnLyUldmlld0dRJmxhYmVsRidGaG9GL0ZWRlk= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInZHNiI2I0kieEdGJSwkKiZJJF9DMUdGJSIiIkYnIiIkI0YrRiw= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EnYHlfXzNgRictSSNtb0dGJDYtUSomY29sb25lcTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjRRJ2l0YWxpY0YnLUYwNi1RKCZzcmFycjtGJ0YzRjZGOUY7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklGVi1GLDYlUSVldmFsRidGTUZQLUkobWZlbmNlZEdGJDYkLUYjNictRiw2I1EnYHlfXzJgRictRmZuNiQtRiM2I0ZKRjMtRjA2LVEiLEYnRjNGNi9GOkZPRjtGPUY/RkFGQ0ZVL0ZJUSwwLjMzMzMzMzNlbUYnLUkobWFjdGlvbkdGJDYlLUkqbXZlcmJhdGltR0YkNiNRUC8tSSJ2RzYiNiNJInhHNiIsJComSSRfQzFHNiIiIiJJInhHNiIiIiQjIiIiIiIkRicvJSthY3Rpb250eXBlR1E7bWFwbGVzb2Z0LmNvbTpsYWJlbChMMzUyNSlGJy8lJXZpZXdHUSZsYWJlbEYnLUYsNiNRIUYnRjMtRjA2LVEiOkYnRjNGNkY5RjtGPUY/RkFGQ0ZFRkg= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Thus, the solution is: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCYqKEkkX0MxRzYiIiIiSSJ4R0YlIiIkLCZGJ0YmRiZGJiEiIiNGJkYoKiZJI0MyR0YlRiZGKUYqRiY= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRzeXNHRig2JC8sJkkkX0MxR0YoIyIiIiIiJ0kjQzJHRigjRjMiIiMiIiEvLCZGMSMiIiYiIzdGNSMhIiIiIiUjIiIkRjc3JEYvRjk= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRzb2xHRig8JC9JI0MyR0YoISIiL0kkX0MxR0YoIiIkNyNGLg== JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElc3Vic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRJHNvbEYnRi9GMi1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieUYnRi9GMi1GNjYkLUYjNiMtRiw2JVEieEYnRi9GMkZBRkE= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCYqJCwmSSJ4RzYiIiIiRidGJyEiIkYoKiZGJSIiJEYkRihGJw== JSFH
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 2</Text-field> Given 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 Find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTYwO0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0Y/Rj9GPw==
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field> 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 JSFHJSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwkKiYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiVGJiIiIkYnISIiRjA= JSFH
Using Euler we find the solution for the homogeneous equation: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEkbGhzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEkT0RFRidGL0YyL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQtSSNtbkdGJDYkUSIwRidGPQ== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvLCYqJkkieEdGKCIiIy1JJWRpZmZHRiY2JC1JInlHRig2I0YvLUkiJEdGJjYkRi9GMCIiIkY6KiZGL0Y6LUYyNiRGNEYvRjpGMCIiITcjLywmKiZGL0YwLUYyNiRGPEYvRjpGOkY7RjBGPg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHlfX2hgRictSSNtb0dGJDYtUSomY29sb25lcTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1GLDYlUSRyaHNGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNFEnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSdkc29sdmVGJ0ZNRlAtRlM2JC1GIzYlLUYsNiNRIUYnLUkobWFjdGlvbkdGJDYlLUkqbXZlcmJhdGltR0YkNiNRZXQvLCYqJkkieEc2IiIiIy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkieUc2IjYjSSJ4RzYiSSJ4RzYiSSJ4RzYiIiIiIiIiKiZJInhHNiIiIiItSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkieUc2IjYjSSJ4RzYiSSJ4RzYiIiIiIiIjIiIhRicvJSthY3Rpb250eXBlR1E7bWFwbGVzb2Z0LmNvbTpsYWJlbChMMjkyOClGJy8lJXZpZXdHUSZsYWJlbEYnRmhuRjNGMw== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSV5X19oR0YoLCZJJF9DMUdGKCIiIiomSSRfQzJHRihGMEkieEdGKCEiIkYwNyNGLg== Using the parameter variation we find the private solution:JSFHJSFH 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 Thus: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder PCQvSSNDMUc2IiIiIS9JI0MyR0YlRiY= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElc3Vic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiNRIUYnLUkobWFjdGlvbkdGJDYlLUkqbXZlcmJhdGltR0YkNiNROTwkL0kjQzFHNiIiIiEvSSNDMkc2IiIiIUYnLyUrYWN0aW9udHlwZUdRO21hcGxlc29mdC5jb206bGFiZWwoTDM2MjkpRicvJSV2aWV3R1EmbGFiZWxGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGUi8lKnN5bW1ldHJpY0dGUi8lKGxhcmdlb3BHRlIvJS5tb3ZhYmxlbGltaXRzR0ZSLyUnYWNjZW50R0ZSLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieUYnRi9GMi1GNjYkLUYjNiMtRiw2JVEieEYnRi9GMkZORk4= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCQqJi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ4R0YpIiIiRishIiJGLQ== 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder KiRJI1BpRyUqcHJvdGVjdGVkRyEiIg== JSFH
JSFH
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 3</Text-field> Find the homogeneous equation that its solutions are: 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
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field> 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 JSFH JSFH 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 We write a determinant of the solutions: JSFHJSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LyIiIUYj JSFH
JSFH and that is the original equation.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFH
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 4</Text-field> Given 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 find the solution for 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
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0ZULyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUYsNiVRKmludGVyZmFjZUYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRLHR5cGVzZXR0aW5nRidGL0YyLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUYsNiVRKWV4dGVuZGVkRidGL0YyRjlGNUZPLUZQNiZGUkZVRlgvRmVuUSVhdXRvRictRiw2JVEld2l0aEYnRi9GMi1GW282JC1GIzYjLUYsNiVRKERFdG9vbHNGJ0YvRjJGOUY1RmhvLUYsNiNRIUYn JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwoLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJEYnISIiIiIiKiZGKUYxRidGMUYxKiZGKUYxRiciIiNGMQ== JSFH
Using the "Constant coefficient" method, writing the Characteristic polynomial:JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRzb2xHRig2JSEiIkYvRi83JUYvRi9GLw== Thus, our LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== is: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GNjYmLUYjNiMtRiw2JVEkSUNTRidGL0YyL0YzUSdub3JtYWxGJy8lJW9wZW5HUSJ8ZnJGJy8lJmNsb3NlR1EifGhyRidGQQ== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder PCUvSSNDMUc2IiIiIi9JI0MyR0YlRiYvSSNDM0dGJUYm JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCgtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ4R0YoISIiIiIiKiZGI0YtRitGLUYtKiZGI0YtRisiIiNGLQ== JSFH
JSFHJSFH
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 5</Text-field> Find the General solution of the given equation: 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
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field> 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 JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwwLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJEYnIiImIyEiIiIlK0UqJEYnIiIjI0YyIiM1KiZJJF9DMUdGJSIiIi1JJGV4cEdGK0YmRjpGOiomSSRfQzJHRiVGOi1GPDYjLCRGJ0YyRjpGMiooSSRfQzNHRiVGOi1GKjYjKiZGMCNGOkY1RidGOkY6RjBGRyNGOkYwKihJJF9DNEdGJUY6LUkkY29zR0YrRkVGOkYwRkcjRjJGMEkkX0M1R0YlRjo= JSFH
JSFH First we find the solution of the homogeneous equation: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEkbGhzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEkT0RFRidGL0YyL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQtSSNtbkdGJDYkUSIwRidGPQ== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvLCgtSSVkaWZmR0YmNiQtSSJ5R0YoNiNJInhHRigtSSIkR0YmNiRGNCIiJiIiIi1GLzYkRjEtRjY2JEY0IiIkIiIlLUYvNiRGMUY0ISImIiIhNyMvLCgtRi82JC1GLzYkLUYvNiQtRi82JEZARjRGNEY0RjRGOUZLRj9GQEZCRkM= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwsSSRfQzFHRiUiIiIqJkkkX0MyR0YlRiotSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IywkRichIiJGKkYqKiZJJF9DM0dGJUYqLUYuRiZGKkYqKiZJJF9DNEdGJUYqLUkkc2luR0YvNiMqJiIiJiNGKiIiI0YnRipGKkYqKiZJJF9DNUdGJUYqLUkkY29zR0YvRjxGKkYq Now we look for the private solution: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVPREUxR0YoLywoLUklZGlmZkdGJjYkLUkieUdGKDYjSSJ4R0YoLUkiJEdGJjYkRjYiIiYiIiItRjE2JEYzLUY4NiRGNiIiJCIiJS1GMTYkRjNGNiEiJkY2NyMvLCgtRjE2JC1GMTYkLUYxNiQtRjE2JEZCRjZGNkY2RjZGO0ZMRkFGQkZERjY= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVElT0RFMkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJGxoc0YnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRJE9ERUYnRi9GMkY5LUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZbby1GLDYlUSRjb3NGJy9GMEY9RjktRlM2JC1GIzYjLUYsNiVRInhGJ0YvRjJGOQ== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVPREUyR0YoLywoLUklZGlmZkdGJjYkLUkieUdGKDYjSSJ4R0YoLUkiJEdGJjYkRjYiIiYiIiItRjE2JEYzLUY4NiRGNiIiJCIiJS1GMTYkRjNGNiEiJiwkLUkkY29zR0YlRjUhIiI3Iy8sKC1GMTYkLUYxNiQtRjE2JC1GMTYkRkJGNkY2RjZGNkY7RlBGQUZCRkRGRQ== 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LDAqJEkieEc2IiIiIyMhIiIiIiYqJkkkX0MxR0YlIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNGJEYsRiYqJkkkX0MyR0YlRiwtRi42IywkRiRGKEYsISIjKihJJF9DM0dGJUYsLUkkc2luR0YvNiMqJkYpI0YsRiZGJEYsRixGKUY/I0YmRikqKEkkX0M0R0YlRiwtSSRjb3NHRi9GPUYsRilGPyNGOEYpSSRfQzVHRiVGJi1GPDYjLCRGJEYpI0YoIiUrRQ== We add the homogeneous solution: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSw4SSRfQzFHRiUiIiIqJkkkX0MyR0YlRiotSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IywkRichIiJGKkY0KiZJJF9DM0dGJUYqLUYuRiZGKkYqKiZJJF9DNEdGJUYqLUkkc2luR0YvNiMqJiIiJiNGKiIiI0YnRipGKkYqKiZJJF9DNUdGJUYqLUkkY29zR0YvRjxGKkYqKiRGJ0ZAI0Y0Rj4qJkYpRipGN0YqRkAqKEY2RipGOkYqRj5GPyNGQEY+KihGOUYqRkNGKkY+Rj8jISIjRj5GQkZALUY7NiMsJEYnRj4jRjQiJStF JSFH
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 6</Text-field> Find the solution: 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
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field> 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 JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwqLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJEYnISIiIiIiKiZGKUYxRidGMSNGMSIiIy1JJHNpbkdGK0YmI0YwRjRGJ0Yx
Use the same method as in Exercise 5. JSFH
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<Text-field style="Heading 1" layout="Heading 1">Question 7</Text-field> Find the General solutions of: 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
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field> 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 JSFH JSFH JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSw0KiYtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiVGJiIiIi1JI2xuR0YsNiMsJkYvRi9GKkYvRi8hIiJGMEY0Ri9GLyomLUYxNiMiIiNGL0YqRi9GNComLUYxNiMsJC1JJGNvc0dGLEYmRjhGL0YqRi9GLy1GMTYjKiYsJiokRj1GOEYvKiRGM0Y4Ri9GLywmRkNGLyokLCZGKkYvRjRGL0Y4Ri9GNCNGL0Y4KiZGPUYvSSRfQzJHRiVGL0Y0KiZGKkYvSSRfQzFHRiVGL0YvSSRfQzNHRiVGLw== 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwwKiYtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiVGJiIiIi1JI2xuR0YsNiMtSSRjb3NHRixGJkYvRi8qJkYqRi8tRjE2IywmRi9GL0YqRi9GLyEiIiomRjNGL0kkX0MyR0YlRi9GOSomRipGL0kkX0MxR0YlRi9GL0YwRjlJJF9DM0dGJUYvRi9GLw== JSFH
Method: First we solve the homogeneous equation: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnZHNvbHZlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEkbGhzRidGL0YyLUY2NiQtRiM2Iy1GLDYlUSRPREVGJ0YvRjIvRjNRJ25vcm1hbEYnRkQ= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwoSSRfQzFHRiUiIiIqJkkkX0MyR0YlRiotSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiVGJkYqRioqJkkkX0MzR0YlRiotSSRjb3NHRi9GJkYqRio= Now we can use the Parameter variation to find the private solutions: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJXR0YoLUknUlRBQkxFR0YoNiUiNTVoPXNWMlduVz0tSSdNQVRSSVhHRig2IzclNyUiIiItSSRzaW5HRiU2I0kieEdGKC1JJGNvc0dGJUY6NyUiIiFGPCwkRjghIiI3JUY/RkAsJEY8RkFJJ01hdHJpeEdGJTcjLUZENiMvSSQlaWRHRihGMQ== 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNEZUdGKCEiIjcjRi4= JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNXMUdGKC1JJ1JUQUJMRUdGKDYlIjVJJyk9c1YyV25XPS1JJ01BVFJJWEdGKDYjNyU3JSIiIS1JJHNpbkdGJTYjSSJ4R0YoLUkkY29zR0YlRjo3JUY3RjwsJEY4ISIiNyUiIiJGPywkRjxGQEknTWF0cml4R0YlNyMtRkQ2Iy9JJCVpZEdGKEYx 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSREZTFHRighIiI3I0Yu JSFH LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+LUklZGlmZkdGJjYkLUkjQzFHRig2I0kieEdGKEYzLUkkdGFuR0YlRjI3I0Y0 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNDMUdGKCwkLUkjbG5HRiU2Iy1JJGNvc0dGJTYjSSJ4R0YoISIiNyNGLg== JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNXMkdGKC1JJ1JUQUJMRUdGKDYlIjUlKls9c1YyV25XPS1JJ01BVFJJWEdGKDYjNyU3JSIiIiIiIS1JJGNvc0dGJTYjSSJ4R0YoNyVGOEY4LCQtSSRzaW5HRiVGOyEiIjclRjhGNywkRjlGQUknTWF0cml4R0YlNyMtRkQ2Iy9JJCVpZEdGKEYx 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSREZTJHRigtSSRzaW5HRiU2I0kieEdGKDcjRi4= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+LUklZGlmZkdGJjYkLUkjQzJHRig2I0kieEdGKEYzLCQqJi1JJHRhbkdGJUYyIiIiLUkkc2luR0YlRjJGOCEiIjcjRjQ= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNDMkdGKCwmLUkkc2luR0YlNiNJInhHRigiIiItSSNsbkdGJTYjLCYtSSRzZWNHRiVGMUYzLUkkdGFuR0YlRjFGMyEiIjcjRi4= JSFH JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNXM0dGKC1JJ1JUQUJMRUdGKDYlIjU9Oj1zVjJXblc9LUknTUFUUklYR0YoNiM3JTclIiIiLUkkc2luR0YlNiNJInhHRigiIiE3JUY8LUkkY29zR0YlRjpGPDclRjwsJEY4ISIiRjdJJ01hdHJpeEdGJTcjLUZDNiMvSSQlaWRHRihGMQ== 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSREZTNHRigtSSRjb3NHRiU2I0kieEdGKDcjRi4= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+LUklZGlmZkdGJjYkLUkjQzNHRig2I0kieEdGKEYzLCQqJi1JJHRhbkdGJUYyIiIiLUkkY29zR0YlRjJGOCEiIjcjRjQ= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNDM0dGKC1JJGNvc0dGJTYjSSJ4R0YoNyNGLg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= JSFH
We sum it all up: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkieUdGKDYjSSJwR0YoLCgtSSNsbkdGJTYjLUkkY29zR0YlNiNJInhHRighIiIqJiwmLUkkc2luR0YlRjciIiItRjM2IywmLUkkc2VjR0YlRjdGPi1JJHRhbkdGJUY3Rj5GOUY+RjxGPkY+KiRGNSIiI0Y+NyNGMQ== JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LDAqJkkkX0MzRzYiIiIiLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNJInhHRiVGJkYmKiYtSSRzaW5HRilGLEYmLUkjbG5HRik2IywmRiZGJkYvRiZGJiEiIiomRi9GJi1GMjYjRidGJkYmKiZJJF9DMkdGJUYmRi9GJkYmRjdGNUkkX0MxR0YlRiZGJkYm JSFH
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 8</Text-field> Find a general solution for: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field> 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 JSFH print(); # input placeholder NiI= JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwqKigtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJUYmIiIiLUkkZXhwR0YsRiZGL0YnRi8hIiIqJkkkX0MxR0YlRi9GMEYvRi8qKEkkX0MyR0YlRi9GMEYvRidGL0YvKihJJF9DM0dGJUYvRjBGL0YnIiIjRi8=
Method: We first solve the homogeneous equation: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnZHNvbHZlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiYtRiw2JVEkbGhzRidGL0YyLUY2NiQtRiM2Iy1GLDYlUSRPREVGJ0YvRjIvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiPUYnRkQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkwvJSlzdHJldGNoeUdGTC8lKnN5bW1ldHJpY0dGTC8lKGxhcmdlb3BHRkwvJS5tb3ZhYmxlbGltaXRzR0ZMLyUnYWNjZW50R0ZMLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGZW4tSSNtbkdGJDYkUSIwRidGREZE LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwoKiZJJF9DMUdGJSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJUYmRitGKyooSSRfQzJHRiVGK0YsRitGJ0YrRisqKEkkX0MzR0YlRitGLEYrRiciIiNGKw== We find the private solution the same way we did in exercise 7, sum them up, and get to the solution we found in 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwqKigtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJUYmIiIiLUkkZXhwR0YsRiZGL0YnRi8hIiIqJkkkX0MxR0YlRi9GMEYvRi8qKEkkX0MyR0YlRi9GMEYvRidGL0YvKihJJF9DM0dGJUYvRjBGL0YnIiIjRi8=
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<Text-field style="Heading 1" layout="Heading 1">Question 9</Text-field> 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 JSFH JSFH print(); # input placeholder NiI= Given: 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 JSFHJSFH Three private solutions of the equation 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. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSIsRidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJxRidGL0YyRjVGPy1GLDYlUSJmRidGL0YyRjVGPQ== are continuous functions for any LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== is a solution of the given equation and ICS are: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEkSUNTRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUYsNi1RKiZjb2xvbmVxO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZTLUZHNiVRInlGJ0ZKRk0tSShtZmVuY2VkR0YkNiQtRiM2Iy1JI21uR0YkNiRRIjBGJ0YvRi8tRiw2LVEiPUYnRi9GMkY1RjdGOUY7Rj1GP0ZSRlQtRmhuNiRRIjFGJ0YvLUYsNi1RIixGJ0YvRjIvRjZGTEY3RjlGO0Y9Rj9GQS9GRVEsMC4zMzMzMzMzZW1GJ0YrRlUtRiw2LVEiJ0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4xMTExMTExZW1GJ0ZERlhGW29GXm8tRiw2LVEiOkYnRi9GMkY1RjdGOUY7Rj1GP0ZSRlQ= Find 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
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field> We know that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSIsRidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJxRidGL0YyRjVGPy1GLDYlUSJmRidGL0YyRjVGPQ== are continuous. So we can find the equation by subtracting private solutions: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCYtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieEdGKCEiIy1JJGNvc0dGJUYpIiIm 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCYtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieEdGKCEiJC1JJGNvc0dGJUYpIiIm Thus: 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 We found the equation and know the ICS:JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder PCQvSSNDMUc2IiIiIi9JI0MyR0YlRiY= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElc3Vic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiNRIUYnLUkobWFjdGlvbkdGJDYlLUkqbXZlcmJhdGltR0YkNiNROTwkL0kjQzFHNiIiIiIvSSNDMkc2IiIiIkYnLyUrYWN0aW9udHlwZUdRO21hcGxlc29mdC5jb206bGFiZWwoTDMzMjYpRicvJSV2aWV3R1EmbGFiZWxGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGUi8lKnN5bW1ldHJpY0dGUi8lKGxhcmdlb3BHRlIvJS5tb3ZhYmxlbGltaXRzR0ZSLyUnYWNjZW50R0ZSLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieUYnRi9GMi1GNjYkLUYjNiMtRiw2JVEieEYnRi9GMkZORk4= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCgtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieEdGKCIiIi1JJGNvc0dGJUYpRisqJkYqRitGI0YrRis= JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCYiIiJGI0kjUGlHJSpwcm90ZWN0ZWRHI0YjIiIj
JSFHJSFH
JSFH
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 10</Text-field> Find the General solution for 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 when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field> 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 JSFH JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY/LUkjbWlHRiQ2JVEkT0RFRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSVtc3VwR0YkNiUtRiw2JVEieEYnRi9GMi1GIzYjLUkjbW5HRiQ2JFEiM0YnRjkvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZcby1GLDYlUSJ5RidGL0YyLUY2Ni1RIidGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMTExMTExMWVtRidGXW9GYW9GYW8tRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZqby1GWDYkUSIyRidGOUZobi1GUDYlRlItRiM2I0ZccEZlbkZobkZeb0Zhb0Zhb0Zmb0ZSRmhuRl5vRmFvLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSEZpb0ZbcEZeby1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1GWDYkRmduRjktRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGXG8vJSZkZXB0aEdGY3EvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRiw2JVEnZHNvbHZlRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiNGK0Y5 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwoKiZJJF9DMUdGJSIiIkYnRitGKyomSSRfQzJHRiVGKy1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjbG5HRjBGJkYrRisqJkkkX0MzR0YlRistSSRjb3NHRjBGM0YrRis=
Method: Using Euler:JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRzb2xHRig2JSIiIl4jRi9eIyEiIjclRi9GMEYx Knowing that 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 we get the next solution: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCgqJkkjQzFHNiIiIiJJInhHRiVGJkYmKiZJI0MyR0YlRiYtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2Iy1JI2xuR0YsNiNGJ0YmRiYqJkkjQzNHRiVGJi1JJGNvc0dGLEYvRiZGJg== and we can see that the answer is what we found at
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<Text-field style="Heading 1" layout="Heading 1">Question 11</Text-field> Solve 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 Also, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=.
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field> 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 JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwmKiZGJyIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjbG5HRi1GJkYqISIiKiRGJyIiJEYq JSFH
Method: First we find the homogeneous solution: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnZHNvbHZlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEkbGhzRidGL0YyLUY2NiQtRiM2Iy1GLDYlUSRPREVGJ0YvRjIvRjNRJ25vcm1hbEYnRkQ= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kieEdGJSwmKihJJF9DMUdGJSIiIkYnRistSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2Iy1JI2xuR0YuRiZGK0YrKihJJF9DMkdGJUYrRidGKy1JJGNvc0dGLkYxRitGKw== 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSV5X19oR0YoLCYqKEkkX0MxR0YoIiIiSSJ4R0YoRjEtSSRzaW5HRiU2Iy1JI2xuR0YlNiNGMkYxRjEqKEkkX0MyR0YoRjFGMkYxLUkkY29zR0YlRjVGMUYxNyNGLg== Find a private solution: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EnYHlfX3BgRictSSNtb0dGJDYtUSInRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHUSYwLjBlbUYnLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y0USdpdGFsaWNGJ0Yz LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LCQqJkkiYUc2IiIiIkkieEdGJSIiIyIiJA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHlfX3BgRictSSNtb0dGJDYtUSInRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHUSYwLjBlbUYnRi8tSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjRRJ2l0YWxpY0YnRjM= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LCQqJkkiYUc2IiIiIkkieEdGJUYmIiIn JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); 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# input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJ5R0YoLCgqKEkkX0MxR0YoIiIiSSJ4R0YoRjEtSSRzaW5HRiU2Iy1JI2xuR0YlNiNGMkYxRjEqKEkkX0MyR0YoRjFGMkYxLUkkY29zR0YlRjVGMUYxKiRGMiIiJEYxNyNGLg== 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder PCQvSSRfQzFHNiIiIiEvSSRfQzJHRiUhIiI= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCYqJkkieEc2IiIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkjbG5HRik2I0YkRiYhIiIqJEYkIiIkRiY= JSFH
JSFH JSFH