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Transformation of a Cauchy-Euler equation

  1. Mar 26, 2013 #1
    1. The problem statement, all variables and given/known data
    x2y'' - xy' = ln x

    2. Relevant equations
    The problem I'm having is what do I do with x = et or t = ln x.

    3. The attempt at a solution
    I know you have to start with x = et or t = ln x however I'm not sure what to do next...
  2. jcsd
  3. Mar 26, 2013 #2
    You need to express ## y' = \frac {dy} {dx}, \ y'' = \frac {d^2y} {dx^2} ## in terms of ## \frac {dy} {dt} ## and ## \frac {d^2y} {dt^2} ##.
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