Exact - Maple Help

Student[ODEs][Solve]

 Exact
 Solve a first order exact ODE

 Calling Sequence Exact(ODE, y(x))

Parameters

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

Description

 • 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.

Examples

 > $\mathrm{with}\left({{\mathrm{Student}}_{\mathrm{ODEs}}}_{\mathrm{Solve}}\right):$
 > $\mathrm{ode1}≔2xy\left(x\right)-9{x}^{2}+\left(2y\left(x\right)+{x}^{2}+1\right)\left(\frac{ⅆ}{ⅆx}y\left(x\right)\right)=0$
 ${\mathrm{ode1}}{≔}{2}{}{x}{}{y}{}\left({x}\right){-}{9}{}{{x}}^{{2}}{+}\left({2}{}{y}{}\left({x}\right){+}{{x}}^{{2}}{+}{1}\right){}\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right)\right){=}{0}$ (1)
 > $\mathrm{Exact}\left(\mathrm{ode1},y\left(x\right)\right)$
 $\left\{{y}{}\left({x}\right){=}{-}\frac{{{x}}^{{2}}}{{2}}{-}\frac{{1}}{{2}}{-}\frac{\sqrt{{{x}}^{{4}}{+}{12}{}{{x}}^{{3}}{+}{2}{}{{x}}^{{2}}{+}{4}{}{\mathrm{_C1}}{+}{1}}}{{2}}{,}{y}{}\left({x}\right){=}{-}\frac{{{x}}^{{2}}}{{2}}{-}\frac{{1}}{{2}}{+}\frac{\sqrt{{{x}}^{{4}}{+}{12}{}{{x}}^{{3}}{+}{2}{}{{x}}^{{2}}{+}{4}{}{\mathrm{_C1}}{+}{1}}}{{2}}\right\}$ (2)

Compatibility

 • The Student[ODEs][Solve][Exact] command was introduced in Maple 2021.
 • The Student[ODEs][Solve][Exact] command was updated in Maple 2022.
 • The output option was introduced in Maple 2022.