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Seperation of variables

  1. Mar 11, 2008 #1
    when is the seperation of variables technique for partial differential equations valid? it seems to give a particular general solution (such as a general fourier series, or series of legendre polynomials) to a problem depending which coordinate system that you are in?
  2. jcsd
  3. Mar 11, 2008 #2


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    Any time your equation is linear. Separation of variables works as long as it is possible to "disassemble" your equation, solve each part, then put them back together into a solution of the entire equation. That is basically what "linear" allows us to do.
  4. Mar 16, 2008 #3
    I think that's a little strong since not every linear partial differential equation is separable.
  5. Mar 16, 2008 #4
    I wonder what the conditions are. Would all first order linear PDEs be separable? If there was a forcing function could we just deal with the homogeneous part like we can for ODEs?
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