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Math Help - first order pde

  1. #1
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    first order pde

    Hi, need some help here so thanks to any replies.

    PDE: yu_x+2xyu_y=y^2

    a) characteristic equations:
    dx/ds=y, dy/ds=2xy, du/ds=y^2

    b) find dy/dx and solve

    dy/dx=dy/ds * ds/dx = x/y
    ydy=xdx
    y^2/2=x^2/2 +c
    y=\pm \sqrt{x^2+2c}

    c) general solution

    d) solve PDE

    e) find u(x,y)
    here I should be finding du/ds and solve after letting x(s)=? and y(s)=?

    I need some help, so thanks guys.
    Last edited by blackthunder; March 18th 2012 at 05:19 AM.
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