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Math Help - Characteristics ... obtain a general solution

  1. #1
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    Characteristics ... obtain a general solution

    Obtain a general solution of

    x^2(dU/dx) + y^2(dU/dy) = (x+y)U

    Hint: Note that the characteristics imply

    dy/y^2 = (dx-dy)/(x^2-y^2)

    My attempt:

    (x^2 - y^2)dy = y^2(dx-dy)
    x^2dy - y^2dy = y^2dx - y^2dy
    x^2dy = y^2dx.

    Integrating both sides gives

    x^2y = y^2x + c

    where I get stuck
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