Solve an Ordinary Differential Equation - Maple Programming Help

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Solve an Ordinary Differential Equation

 Description Solve an ordinary differential equation (ODE).

Enter an ODE.

 > $\left({t}{+}{1}\right)\frac{{{ⅆ}}^{{2}}}{{ⅆ}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{{t}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{v}\left({t}\right){+}\frac{{ⅆ}}{{ⅆ}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{v}\left({t}\right){-}{4}{t}{=}{0}$
 $\left({t}{+}{1}\right){}\left(\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{t}}^{{2}}}{}{v}{}\left({t}\right)\right){+}\frac{{ⅆ}}{{ⅆ}{t}}{}{v}{}\left({t}\right){-}{4}{}{t}{=}{0}$ (1)

Enter the initial conditions for the ODE.

 > ${v}\left({0}\right){=}{5}{,}{\mathrm{D}}\left({v}\right)\left({0}\right){=}{3}$
 ${v}{}\left({0}\right){=}{5}{,}{\mathrm{D}}{}\left({v}\right){}\left({0}\right){=}{3}$ (2)

Solve the ODE.

 > $\mathrm{dsolve}(\left[,\right])$
 ${v}{}\left({t}\right){=}{{t}}^{{2}}{-}{2}{}{t}{+}{5}{}{\mathrm{ln}}{}\left({t}{+}{1}\right){+}{5}$ (3)

Alternatively, you can use the ODE Analyzer assistant, a point-and-click interface. There are two ways to launch this assistant.

 • Enter an ODE.  Then, from the context menu select Solve DE Interactively.
 • Enter an ODE and initial conditions for the function and its derivative at a given point, then click the following ODE Analyzer button.
 >

For more information on the ODE Analyzer Assistant, see the Using the Interactive ODE Analyzer Assistant.

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