text: 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
  
   > $\mathrm{with}\left({{\mathrm{Student}}_{\mathrm{ODEs}}}_{\mathrm{Solve}}\right):$
   > $\mathrm{ode1}≔{t}^{2}\left(z\left(t\right)+1\right)+{z\left(t\right)}^{2}\left(t-1\right)\left(\frac{ⅆ}{ⅆt}z\left(t\right)\right)=0$
   ${\mathrm{ode1}}{≔}{{t}}^{{2}}{}\left({z}{}\left({t}\right){+}{1}\right){+}{{z}{}\left({t}\right)}^{{2}}{}\left({t}{-}{1}\right){}\left(\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{z}{}\left({t}\right)\right){=}{0}$ (1)
   > $\mathrm{FirstOrder}\left(\mathrm{ode1},z\left(t\right)\right)$
   $\frac{{{z}{}\left({t}\right)}^{{2}}}{{2}}{-}{z}{}\left({t}\right){+}{\mathrm{ln}}{}\left({z}{}\left({t}\right){+}{1}\right){=}{-}\frac{{{t}}^{{2}}}{{2}}{-}{t}{-}{\mathrm{ln}}{}\left({t}{-}{1}\right){+}{\mathrm{_C1}}$ (2)
  
  Compatibility
  
   • The Student[ODEs][Solve][FirstOrder] command was introduced in Maple 2021.
   • The Student[ODEs][Solve][FirstOrder] command was updated in Maple 2022.
   • The output option was introduced in Maple 2022.