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Visualizing the Solution of Two Linear Differential Equations

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The analytical solutions of the two differential equations and , subject to the initial conditions and are used to create two plots, a parametric plot of a curve with horizontal coordinate and vertical coordinate and a standard plot of and as functions of from 0 to .

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The initial conditions and are set by locators on the parametric plot; you can use more than one. A locator's horizontal and vertical coordinates give and , respectively. After changing from the parametric plot to the standard plot, locators appear on the standard plot if and is in the plot range.

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Contributed by: Mikhail Dimitrov Mikhailov (March 2011)
Open content licensed under CC BY-NC-SA

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The expressions for and given by the Mathematica built-in function DSolve are not applicable when . For this special case the solutions are simplified using Mathematica's Limit function. Thus our function twoDSolve correctly computes and for all parameters specified.

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