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Differential equation question

  1. Oct 14, 2011 #1
    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?
     
  2. jcsd
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