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Solve equation using the Method of Characteristics

  1. Oct 9, 2008 #1
    1. Solve the following equation using the Method of Characteristics

    xux +yuy=-u
    subject to u(cos(s), sin(s)) = 1, 0 ≤ s ≤ pi





    2. Relevant equations





    3. Characteristics for this equation are
    dx/dt=x.....(1)
    dy/dt=y.....(2)
    du/dt=-u....(3)
    From(3) get ln(u)=-t+c, u=k*exp(-t)

    But i get stuck on the u(cos(s), sin(s)) = 1, i don't know how to use the initial contidion (u(cos(s), sin(s)) = 1 )to do the (1) and (2).

    Can anyone help me to finish the rest of the question?

    Many thanks








     
    Last edited: Oct 9, 2008
  2. jcsd
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