Solving $z''(x)=a\,z'(x)+b(x)\,z(x)$

Question

Does anybody know a good starting point to solve the ODE

$$z''(x)=a\,z'(x)+b(x)\,z(x) \;,$$

where $a$ is some constant and $b$ some function?

Answer 1

There is no general closed-form solution. You might try power series.