Solving first order linear D.E.s

The simplest general method for solving first order linear D.E.s ( $\frac{dy}{dx}+P(x)y=Q(x)$ ) is to add an additional function $\mu (x)$ :

$\begin{indisplay} \begin{aligned} & D_xy+P(x)y=Q(x) \\ & \Leftrightarrow \mu ... ...\mu} = \ln \mu \Rightarrow \mu (x)=e^{\int P(x)dx} \end{aligned}\end{indisplay}$

And then $\mu (x)$ can be plugged back in to find y.