JSFHMAT2705-02/06 09F Quiz 2 Print Name (Last, First) _________________________________|__Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use arrows and equal signs when appropriate. Always simplify expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation). Indicate where technology is used and what type (Maple, GC).
1.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
initial condition 1: y(0) = 1;
initial condition 2: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiMEYnL0YzUSdub3JtYWxGJ0Y+Rj4tSSNtb0dGJDYtUSI9RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZVRjpGPg==;
initial condition 3: y(0)= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGL0Yv.a) Indicate these initial data points on the graph by circled dots and roughly draw in the corresponding solution curves.b) Find the (almost) general solution of the differential equation. What obvious solution is missing from this family?c) Find the solution which satisfies the first initial condition.d) Evaluate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiMkYnL0YzUSdub3JtYWxGJ0Y+Rj4tRiw2I1EhRidGPg== for this solution and mark the corresponding point on the graph by a circled dot. Is this consistent with your approximate hand drawn solution? 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e) Check by hand that your solution to c) solves the differential equation.f) Enter the differential equation and its initial condition separated by a comma in Maple. Right click and solve. Write down the form of the solution that it gives you. Now right click and choose Simplify, simplify. Does it agree with your hand solution? Can you simplify Maple's solution by hand to get the same result? If so, show the steps.solution1.a)QyQtSSV3aXRoRzYiNiNJKERFdG9vbHNHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiUhIiI=PkkkZGVxRzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ5R0YkNiNJInhHRiRGLSwkKiZGLSIiIkYqIiIjISIjQyc+SSZpbml0c0c2IjwlNyQiIiEhIiI3JEYoRig3JEYoIiIiRiwtSSdERXBsb3RHRiU2KEkkZGVxR0YlLUkieUdGJTYjSSJ4R0YlL0Y0OyEiIyIiIy9GMkY2RiQvSShkaXJncmlkR0YlNyQiI0BGPUYsLUYuNidGMEYxRjVGOUY6b) general solutionLUknZHNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiRJJGRlcUdGJy1JInlHRic2I0kieEdGJw==separable solution steps and initial condition by 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Multiplying through the negative sign and letting LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GUy1GLDYlUSNDMUYnRi9GMkY5 gives: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Since we divided by LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= in the procedure, this family does not contain the obvious solution LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=.c) imposing the first initial condition: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c) first initial conditionQyUtSSdkc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDwkSSRkZXFHRigvLUkieUdGKDYjIiIhIiIiLUYuNiNJInhHRihGMT5JJXNvbDFHRigtSSlzaW1wbGlmeUdGJTYjSSIlR0YoSometimes Maple surprises us, but simplify is a useful operation to keep in mind and apply.d) Evaluating this solution at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk= leads 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So this curve passes through the point 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) Backsubstituting into the DE we check the solution:QyctSSVzdWJzRyUqcHJvdGVjdGVkRzYkLy1JInlHNiI2I0kieEdGKiokLCYqJEYsIiIjIiIiRjFGMSEiIkkkZGVxR0YqRjEtSSlzaW1wbGlmeUc2JEYlSShfc3lzbGliR0YqNiNJIiVHRipGMSwmLUkkbGhzR0YlRjhGMS1JJHJoc0dGJUY4RjI=f) Here is the right click solution and simplification:NiRJJGRlcUc2Ii8tSSJ5R0YkNiMiIiEiIiI=LUknZHNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQ8JC8tSSJ5R0YnNiMiIiEiIiIvLUklZGlmZkdGJTYkLUYsNiNJInhHRidGNiwkKiZGNkYvRjQiIiMhIiM8I0Y0LUkpc2ltcGxpZnlHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy8tSSJ5R0YnNiNJInhHRicsJComLCYhIiIiIiIqJEYtIiIlRjJGMSwmKiRGLSIiIyEiI0Y3RjJGMiNGMUY3