 SeparateVariables - Maple Help

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Student[ODEs]

 SeparateVariables
 separate the dependent and independent variables of an ODE Calling Sequence SeparateVariables(ODE, y(x)) Parameters

 ODE - a first order ordinary differential equation y - name; the dependent variable x - name; the independent variable Description

 • The SeparateVariables(ODE, y(x)) returns an equivalent ODE in a form where the dependent and independent variables are separated. Examples

 > $\mathrm{with}\left({\mathrm{Student}}_{\mathrm{ODEs}}\right):$
 > $\mathrm{ode1}≔{t}^{2}\left(z\left(t\right)+1\right)+{z\left(t\right)}^{2}\left(t-1\right)\left(\frac{ⅆ}{ⅆt}z\left(t\right)\right)=0$
 ${\mathrm{ode1}}{≔}{{t}}^{{2}}{}\left({z}{}\left({t}\right){+}{1}\right){+}{{z}{}\left({t}\right)}^{{2}}{}\left({t}{-}{1}\right){}\left(\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{z}{}\left({t}\right)\right){=}{0}$ (1)
 > $\mathrm{SeparateVariables}\left(\mathrm{ode1},z\left(t\right)\right)$
 $\frac{\left(\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{z}{}\left({t}\right)\right){}{{z}{}\left({t}\right)}^{{2}}}{{z}{}\left({t}\right){+}{1}}{=}{-}\frac{{{t}}^{{2}}}{{t}{-}{1}}$ (2) Compatibility

 • The Student[ODEs][SeparateVariables] command was introduced in Maple 2021.