In practice, if I get a differential equation that I don't recognize and I want a closed-form solution, I check out http://eqworld.ipmnet.ru/ http://eqworld.ipm

In practice, if I get a differential equation that I don't recognize and I want a closed-form solution, I check out http://eqworld.ipmnet.ru/ http://eqworld.ipmnet.ru/ or one of the books produced by the same folks. It's like looking up integrals in an integral table. You look up the form of the equation you want, and they summarize the solution and cite the proof.