Solve a System of Ordinary Differential Equations - Maple Programming Help

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Solve a System of Ordinary Differential Equations

 Description Solve a system of ordinary differential equations (ODEs).

Enter a system of ODEs.

 > $\frac{{ⅆ}}{{ⅆ}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{x}\left({t}\right){=}{y}\left({t}\right){,}\frac{{ⅆ}}{{ⅆ}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}\left({t}\right){=}{-}{x}\left({t}\right)$
 $\frac{{ⅆ}}{{ⅆ}{t}}{}{x}{}\left({t}\right){=}{y}{}\left({t}\right){,}\frac{{ⅆ}}{{ⅆ}{t}}{}{y}{}\left({t}\right){=}{-}{x}{}\left({t}\right)$ (1)

Solve the system of ODEs.

 > $\mathrm{dsolve}\left(\left\{\right\}\right)$
 $\left\{{x}{}\left({t}\right){=}{\mathrm{_C1}}{}{\mathrm{sin}}{}\left({t}\right){+}{\mathrm{_C2}}{}{\mathrm{cos}}{}\left({t}\right){,}{y}{}\left({t}\right){=}{\mathrm{_C1}}{}{\mathrm{cos}}{}\left({t}\right){-}{\mathrm{_C2}}{}{\mathrm{sin}}{}\left({t}\right)\right\}$ (2)
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Alternatively, you can use the ODE Analyzer assistant, a point-and-click interface. There are two ways to launch the assistant.

 • From the Tools menu, select Assistants and then ODE Analyzer.
 • Enter one or more ODEs below, separated by commas, then click the following ODE Analyzer button.
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 Commands Used
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