 MaplePortal/DifferentialEquations - Maple Help

 Differential Equations

 Introduction

Maple solves many types of differential equations. Consider this ODE

 > $\mathrm{de}:=\frac{{ⅆ}^{2}}{ⅆ{t}^{2}}y{}\left(t\right)+\frac{ⅆ}{ⅆt}y{}\left(t\right)+y{}\left(t\right)=3:$
 > $\mathrm{ic}:=\mathrm{D}{}\left(y\right){}\left(0\right)=3,y{}\left(0\right)=4:$

 Symbolic Solution

Maple will give you a symbolic solution...

 > $\mathrm{sol}:=\mathrm{dsolve}{}\left(\left\{\mathrm{de},\mathrm{ic}\right\}\right)$

${\mathrm{sol}}{≔}{y}{}\left({t}\right){=}\frac{{7}{}{{ⅇ}}^{{-}\frac{{t}}{{2}}}{}{\mathrm{sin}}{}\left(\frac{\sqrt{{3}}{}{t}}{{2}}\right){}\sqrt{{3}}}{{3}}{+}{{ⅇ}}^{{-}\frac{{t}}{{2}}}{}{\mathrm{cos}}{}\left(\frac{\sqrt{{3}}{}{t}}{{2}}\right){+}{3}$

 Numeric Solution

...and a numeric solution

 > $\mathrm{sol}:=\mathrm{dsolve}\left(\left\{\mathrm{de},\mathrm{ic}\right\},\mathrm{numeric}\right):$
 > $\mathrm{sol}{}\left(3\right)$

$\left[{t}{=}{3.}{,}{y}{}\left({t}\right){=}{3.27537298676751}{,}\stackrel{{\mathbf{.}}}{{y}}{}\left({t}\right){=}{-0.906034403201660}\right]$

You can also solve coupled ODEs, ODEs with black-box functions, DAEs, events. You can also parameterize the solution of ODEs and more.

This app will generate the ODEs of an n-link pendulum, solve the ODEs numerically, and animate the pendulum

 Number of Links Time Step Number of Frames Applications    