1. The problem statement, all variables and given/known data Solve the following DE using two different methods. ey +ycos(x) +(xey +sin(x))y' =0 2. Relevant equations Exact method, and substitution method. 3. The attempt at a solution I can solve this using the exact method just fine. The second way I'm expected to solve this is by substitution. In the solution it says to use the substitution u = xey +ysinx Once I do that I can solve it just fine. My question is how am I possibly supposed to look at the original equation and think to use that seemingly random substitution. There's quite a few examples where I have to solve using substitutions but I have no idea where these substitutions come from. Is there some method or something I'm supposed to look for that I'm missing here?