Systems of ODEs - Maple Help

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

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