Find all the solutionsof the equation:
$$y'+ay=b(x),\ 0<x<\infty,\ $$
where $a$ is a constant and $b(x)=1$ for $0\le x\le \alpha$, and $b(x)=0$ for $x\gt \alpha$ and $\alpha$ here is a positive constant.
Well, I really got stuck on this problems where the right hand side of the differential equation $b(x)$ is not continuous. Could anyone give me some hints on this, please?