\[ y^{\prime }+p\left ( x\right ) y=q\left ( x\right ) \] ode internal name "linear"
Solved by finding integration factor \(\mu =e^{\int p\left ( x\right ) dx}\). The ode then becomes \(\frac {d}{dx}\left ( \mu y\right ) =\mu q\). Integrating gives \(\mu y=\int \mu qdx+c\) or \[ y=\frac {1}{\mu }\left ( \int \mu qdx+c\right ) \]