I am trying to solve the ODE $y'-axy=b$, where $a$ and $b$ are constants. For $b=0$, the eqn is separable, but for $b\ne 0$ I tried to use an integrating factor of $I=\exp (-ax^2/2)$. This leaves me with $y\exp (-ax^2/2) = \int \exp (-ax^2/2) dx + C$. I cannot evaluate the integral on the RHS analytically.

Is there another applicable method that will solve the original ODE in closed form?