setting up a differential equationEPC4: 1.1.27. Write a differential equation of the form 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 that has a function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA= as a solution if:
the tangent to the graph of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn at the point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtaUdGJDYmUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSIsRidGNy9GO1Enbm9ybWFsRicvJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYmUSJ5RidGNEY3RjpGN0ZBRjdGQUY3RkE= passes through the point 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.solution hint: make a generic diagram A picture makes this easy. Imagine the point is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtbkdGJDYlUSIyRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGNEY3LyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRjYvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JVEiMUYnRjRGN0Y0RjdGNEY3RjRGNw== in the plane so the second point is 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, so the slope of the connecting tangent line is 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Draw by hand a rough diagram like: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 have no clue what the actual curve will look like other than the fact that it has to have the blue line as a tangent line. We can then read off the coordinate differences from the black sided triangle, and evaluate the slope!Maple can solve this problem!
We can even visualize its solutions.So the DE is obviously 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 Done! But with Maple we can plow ahead to see if we can solve and visualize this situation. We will find the solution through the point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtbkdGJDYlUSIyRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGNEY3LyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRjYvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JVEiMUYnRjRGN0Y0RjdGNEY3RjRGNw== and then find the rest.We can use the right margin context sensitive menu choice Solve DE to find that Maple cannot find an explicit solution. But with a little advanced knowledge about the command dsolve with the option 'implicit', we can find the implicit solution.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Success! But we can use rules of logs to combine the two logarithmic terms, and then this simplifies a lot! In fact they combine to yield 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 in several steps: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 result is just this very simple result: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Sometimes we have to help Maple simplify its results. Simplification is complicated, especially when absolute values are avoided in Maple expressions, which is meant to work over the complex numbers where the log of negative real numbers makes sense.We can do implicit plotting of multiple solution curves using contourplot.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 jump at the vertical axis has to do with the arctan function, which has a jump across that axis. This jump can be pushed to the negative horizontal axis by using the alternative extended arctan function that we will encounter later. 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making a suggestive plotTo make a "generic" solution plot, we find a particular IVP solution and plot it implicitly. To get started with plotting we will add this initial condition.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But to plot we have to replace LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA= by just LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== for the plotting command: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We could use the menu plotbuilder choice implicitplot to set this up, but bob will go ahead and plot not only the curve but the tangent line and the two points and a useful slope computation triangle showing the changes in the two coordinates.
First the tangent line has slope 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 field?A directionfield plot shows us how these solution curves come about, but since they develop vertical tangents, the numerical solution comes to a halt (the derivative goes infinite).LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRKERFdG9vbHNGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIjpGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVkY9RkA=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=