The Separable(ODE, y(x)) command finds the solution of a first order separable 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.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{ODEs}\right]\left[\mathrm{Solve}\right]\right)\:$

$\mathrm{ode1}≔t^2\left(z\left(t\right)+1\right)+{z\left(t\right)}^2\left(t-1\right)\mathrm{diff}\left(z\left(t\right)\,t\right)=0$

$\mathrm{ode1}≔t^2\left(z\left(t\right)+1\right)+{z\left(t\right)}^2\left(t-1\right)\left(\frac{\ⅆ}{\ⅆt}z\left(t\right)\right)=0$

$\mathrm{Separable}\left(\mathrm{ode1}\,z\left(t\right)\right)$

$\frac{{z\left(t\right)}^2}{2}-z\left(t\right)+\ln \left(z\left(t\right)+1\right)=-\frac{t^2}{2}-t-\ln \left(t-1\right)+\mathrm{\_C1}$

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

For more information on Maple 2021 changes, see Updates in Maple 2021.

The Student[ODEs][Solve][Separable] command was updated in Maple 2022.

The output option was introduced in Maple 2022.

For more information on Maple 2022 changes, see Updates in Maple 2022.