FirstOrder - Maple Help

Student[ODEs][Solve]

 FirstOrder
 Solve a first order ODE

 Calling Sequence FirstOrder(ODE, y(x))

Parameters

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

Description

 • The FirstOrder(ODE, y(x)) command finds the solution of a first order ODE.
 • Use the option output=steps to make this command return an annotated step-by-step solution.  Further control over the format and display of the step-by-step solution is available using the options described in Student:-Basics:-OutputStepsRecord.  The options supported by that command can be passed to this one.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{ODEs}\right]\left[\mathrm{Solve}\right]\right):$
 > $\mathrm{ode1}≔{t}^{2}\left(z\left(t\right)+1\right)+{z\left(t\right)}^{2}\left(t-1\right)\mathrm{diff}\left(z\left(t\right),t\right)=0$
 ${\mathrm{ode1}}{≔}{{t}}^{{2}}{}\left({z}{}\left({t}\right){+}{1}\right){+}{{z}{}\left({t}\right)}^{{2}}{}\left({t}{-}{1}\right){}\left(\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{z}{}\left({t}\right)\right){=}{0}$ (1)
 > $\mathrm{FirstOrder}\left(\mathrm{ode1},z\left(t\right)\right)$
 $\frac{{{z}{}\left({t}\right)}^{{2}}}{{2}}{-}{z}{}\left({t}\right){+}{\mathrm{ln}}{}\left({z}{}\left({t}\right){+}{1}\right){=}{-}\frac{{{t}}^{{2}}}{{2}}{-}{t}{-}{\mathrm{ln}}{}\left({t}{-}{1}\right){+}{\mathrm{_C1}}$ (2)

Compatibility

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