Transformation of a Cauchy-Euler equation

  • Thread starter jawhnay
  • Start date
  • #1
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Homework Statement


x2y'' - xy' = ln x




Homework Equations


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


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...
 

Answers and Replies

  • #2
6,054
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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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