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Change of variables in a differential equation in Maple

  1. Dec 3, 2013 #1

    CAF123

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    Gold Member

    1. The problem statement, all variables and given/known data
    Consider the differential equation zZ'' + Z' + γ2 Z = 0, where Z = Z(z). Use the change of variables x = √(z/b) with b a constant to obtain the differential equation Z'' + (1/x)Z' + α2Z = 0, where Z = Z(x) and α= 2γ √b

    2. Relevant equations
    Maple commands

    3. The attempt at a solution
    I tried the following:
    Code (Text):

    with(PDEtools):

    PDE:= ...
    tr:= {z = x^2 b}

    dchange(tr, PDE)
    however, this didn't work, possibly because maple is interpreting b as a variable , but I am not sure how to specify that it is simply a constant. I am not sure whether the above will give me what I want, since I have not specified anywhere that I want in the final DE, Z=Z(x).
    Thanks.
     
  2. jcsd
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