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Homework Help: Another partial differential equation problem

  1. Jan 8, 2009 #1
    1. The problem statement, all variables and given/known data

    Derived the general solution of the given equation by using an appropriate change of variables
    5.) du/dt-2(du/dx)=2
    2. Relevant equations

    du/dx=du/d(alpha)*d(alpha)/dx+du/d(beta)*d(beta)/dx
    du/dt= du/d(alpha)*d(alpha)/dt+du/d(beta)*d(beta)/dt

    3. The attempt at a solution

    not really sure how to determine du/d(alpha),d(alpha)/dx,d(beta)/dx ,d(alpha)/dt,d(beta)/dt

    book says alpha=x+2t, beta=x
     
  2. jcsd
  3. Jan 8, 2009 #2
    [tex]
    \frac{\partial\alpha}{\partial x}=1,\frac{\partial\beta}{\partial x}=1 so
    \[
    \frac{\partial u}{\partial x}=\frac{\partial u}{\partial\alpha}\frac{\partial\alpha}{\partial x}+\frac{\partial u}{\partial\beta}\frac{\partial\beta}
    {\partial x}=\frac{\partialu}{\partialx}=\frac{\partial u}{\partial\alpha}+\frac{\partial u}{\partial\beta}
    \]
    [/tex]
    did that help?
     
  4. Jan 9, 2009 #3
    I probably should have said in the back of the book, they give you alpha and beta. They don't give you the equations for alpha and beta in the problem. I don't understand how to determine alpha and beta.
     
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