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Help with Method of Characteristics - PDE's

  1. Oct 24, 2011 #1
    1. Use the method of characteristics to solve: xux+yuy=1



    2. given condition of u(x,y)=1 when x2+y2=1



    3. I know I need to transpose into the s-t domain. Using: du/ds=uxdx/ds+uydy/ds=aux+buy
    so a=x & b=y...

    please help
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 24, 2011 #2
    I was able to solve for the following:
    du/ds=1 integrate to get u=s+K1
    dx/ds=x integrate to get x=K2es
    dy/ds=y integrate to get y=K3es

    I am unsure how to use the IC's
     
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