LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC8lK2V4ZWN1dGFibGVHRj1GOQ== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJnBsb3RzRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSI6RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlZGPUZA LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRKERFdG9vbHNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIjpGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVkY9RkA= 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 Problem 18: Define the differential equation in the following form: 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 a. Compare Euler's Method with RK4 and the exact solution in plot form: 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 b. Compare Euler's Method with RK4 and the exact solution in numerical form, with absolute error at each step: 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 c. Change the stepsize LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiaEYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRi8vRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dGQC8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk9GPA==by changing the number of steps using the option LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEpbnVtc3RlcHNGJy8lJXNpemVHUSMxNEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GNlEnbm9ybWFsRic= (default is 5): 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 d. Repeat for a smaller interval 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: 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 e. Plot the direction field 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 g. Explore 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 using EulerTutor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUStFdWxlclR1dG9yRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNjItRiw2JVElZGlmZkYnRjRGNy1GOzYkLUYjNictRiw2JVEieUYnRjRGNy1GOzYkLUYjNiQtRiw2JVEidEYnRjRGNy9GOFEnbm9ybWFsRidGUC1JI21vR0YkNi1RIixGJ0ZQLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y2LyUpc3RyZXRjaHlHRlgvJSpzeW1tZXRyaWNHRlgvJShsYXJnZW9wR0ZYLyUubW92YWJsZWxpbWl0c0dGWC8lJ2FjY2VudEdGWC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnRk1GUEZQLUZTNi1RIj1GJ0ZQRlYvRlpGWEZlbkZnbkZpbkZbb0Zdby9GYG9RLDAuMjc3Nzc3OGVtRicvRmNvRmpvLUklbXN1cEdGJDYlLUY7NiQtRiM2JUZGRklGUEZQLUYjNiQtSSNtbkdGJDYkUSIyRidGUEZQLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GUzYtUSgmbWludXM7RidGUEZWRmhvRmVuRmduRmluRltvRl1vL0Zgb1EsMC4yMjIyMjIyZW1GJy9GY29GYHFGTUZSRkYtRjs2JC1GIzYkLUZmcDYkRltxRlBGUEZQRmVvLUZmcDYkUSQwLjRGJ0ZQRlJGTUZlby1GZnA2JFEiMUYnRlBGUEZQRlBGKy8lK2V4ZWN1dGFibGVHRlhGUA==