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Homework Help: [PDE] Transforming Hard Equations into Easier Ones

  1. Feb 24, 2013 #1
    I have a PDE and I have to transform it into an easier one using a substitution:

    [itex]u_t=u_{xx}-\beta u[/itex]

    I am supposed to use the following substitution:

    [itex]u(x,t)=e^{-\beta t}w(x,t)[/itex]

    I am supposed to get something that looks like this:


    Can someone show me the steps?
  2. jcsd
  3. Feb 24, 2013 #2

    Ray Vickson

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    Homework Helper

    Here are the steps. Substitute the form ##u(x,t) = e^{-\beta t}w(x,t)## into all terms of the PDE and collect terms. That means you will need to compute ##u_t## and ##u_{xx}## using standard calculus differentiation rules.
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