How do I find a solution to: $$i p(t)\ddot x-\left[p(t)^2+i\dot p(t)\right]\dot x+2ip(t)^3x=0\ ,$$ where $p(t)$ is some chosen smooth function, and the overdot represents derivative with respect to $t$.
Can anyone see a solution for a particular non-trivial choice of $p(t)$?