Systems of ODEs - Maple Help
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ODE Steps for Systems of ODEs

Overview

 • This help page gives a few examples of using the command ODESteps to solve systems of ordinary differential equations.
 • See Student[ODEs][ODESteps] for a general description of the command ODESteps and its calling sequence.

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{ODEs}\right):$
 > $\mathrm{high_order_ode1}≔\frac{{ⅆ}^{3}}{ⅆ{x}^{3}}y\left(x\right)+3\left(\frac{{ⅆ}^{2}}{ⅆ{x}^{2}}y\left(x\right)\right)+4\left(\frac{ⅆ}{ⅆx}y\left(x\right)\right)+2y\left(x\right)=0$
 ${\mathrm{high_order_ode1}}{≔}\frac{{{ⅆ}}^{{3}}}{{ⅆ}{{x}}^{{3}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right){+}{3}{}\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right){+}{4}{}\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right){+}{2}{}{y}{}\left({x}\right){=}{0}$ (1)
 > $\mathrm{ODESteps}\left(\mathrm{high_order_ode1}\right)$
 > $\mathrm{macro}\left(Y=⟨{y}_{1}\left(x\right),{y}_{2}\left(x\right)⟩\right):$
 > $\mathrm{sys2}≔\frac{\partial }{\partial x}Y=\mathrm{%.}\left(\mathrm{Matrix}\left(\left[\left[7,1\right],\left[-4,3\right]\right]\right),Y\right)$
 ${\mathrm{sys2}}{≔}\left[\begin{array}{c}\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{{y}}_{{1}}{}\left({x}\right)\\ \frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{{y}}_{{2}}{}\left({x}\right)\end{array}\right]{=}{\mathrm{Typesetting}}{:-}{\mathrm{_Hold}}{}\left(\left[{\mathrm{%.}}{}\left({\mathrm{RTABLE}}{}\left({36893628571428174892}{,}\left[\begin{array}{cc}{7}& {1}\\ {-4}& {3}\end{array}\right]{,}{\mathrm{Matrix}}\right){,}\left[\begin{array}{c}{y}_{1}{}\left(x\right)\\ {y}_{2}{}\left(x\right)\end{array}\right]\right)\right]\right)$ (2)
 > $\mathrm{ODESteps}\left(\mathrm{sys2}\right)$
 > $\mathrm{sys3}≔\frac{\partial }{\partial x}Y=\mathrm{.}\left(\mathrm{Matrix}\left(\left[\left[1,2\right],\left[3,2\right]\right]\right),Y\right)+⟨1,{ⅇ}^{x}⟩$
 ${\mathrm{sys3}}{≔}\left[\begin{array}{c}\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{{y}}_{{1}}{}\left({x}\right)\\ \frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{{y}}_{{2}}{}\left({x}\right)\end{array}\right]{=}\left[\begin{array}{c}{{y}}_{{1}}{}\left({x}\right){+}{2}{}{{y}}_{{2}}{}\left({x}\right){+}{1}\\ {3}{}{{y}}_{{1}}{}\left({x}\right){+}{2}{}{{y}}_{{2}}{}\left({x}\right){+}{{ⅇ}}^{{x}}\end{array}\right]$ (3)
 > $\mathrm{ODESteps}\left(\mathrm{sys3}\right)$
 > $\mathrm{sys4}≔\left\{\frac{ⅆ}{ⅆx}w\left(x\right)=w\left(x\right)+2z\left(x\right),\frac{ⅆ}{ⅆx}z\left(x\right)=3w\left(x\right)+2z\left(x\right)+{ⅇ}^{x}\right\}$
 ${\mathrm{sys4}}{≔}\left\{\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{w}{}\left({x}\right){=}{w}{}\left({x}\right){+}{2}{}{z}{}\left({x}\right){,}\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{z}{}\left({x}\right){=}{3}{}{w}{}\left({x}\right){+}{2}{}{z}{}\left({x}\right){+}{{ⅇ}}^{{x}}\right\}$ (4)
 > $\mathrm{ODESteps}\left(\mathrm{sys4}\right)$

 See Also