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Math Help - Solving cauchy initial value problems for Partial differential equations

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    Exclamation Solving cauchy initial value problems for Partial differential equations

    Solve the following Cauchy problem :

    -xux +yuy = 1 for 0<x<y, u=2x on y=3x.

    I managed to get the two constants C1 and C2 as C1 = xy and C2 = lny - u.
    Further to apply the initial conditions i found out the general solution for this equation as

    u(x,y) = lny - f(xy).
    Putting the initial conditions here ,i got f(3x2) = ln(3x) - 2x.
    What i cannot make out is , how do i find the value of f(xy) from the fact that f(3x2) = ln(3x)-2x.

    Need help urgently !
    Last edited by mrmaaza123; February 18th 2013 at 05:04 PM.
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