This is one of the larger areas of the Math Reviews database. Cambridge University Press, Cambridge, 1997. Other web sites with this focus SIAM 's Differential Equations page. Here are the AMS and Goettingen resource pages for area 34. Selected topics at this site Review of terms for classifying first-order ODEs .
Discussion includes being careful about technical requirements assumed.
Using the asymptotics on an ODE to determine the asymptotic behaviour of its solutions . System of DEs which model highly oscillatory motion on a sphere. Analyzing a system of three first-order ODEs . A 2nd order linear equation. How to handle 2nd order ODE with no y' term.