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

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

$\mathrm{ode1}≔2xy\left(x\right)-9x^2+\left(2y\left(x\right)+x^2+1\right)\mathrm{diff}\left(y\left(x\right)\,x\right)=0$

$\mathrm{ode1}≔2xy\left(x\right)-9x^2+\left(2y\left(x\right)+x^2+1\right)\left(\frac{\ⅆ}{\ⅆx}y\left(x\right)\right)=0$

$\mathrm{Exact}\left(\mathrm{ode1}\,y\left(x\right)\right)$

$\left\{y\left(x\right)=-\frac{x^2}{2}-\frac{1}{2}-\frac{\sqrt{x^4+12x^3+2x^2+4\mathrm{\_C1}+1}}{2}\,y\left(x\right)=-\frac{x^2}{2}-\frac{1}{2}+\frac{\sqrt{x^4+12x^3+2x^2+4\mathrm{\_C1}+1}}{2}\right\}$

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

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

The Student[ODEs][Solve][Exact] 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.