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Thread: first order pde

  1. #1
    Mar 2012

    first order pde

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

    PDE: $\displaystyle yu_x+2xyu_y=y^2$

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

    b) find dy/dx and solve

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

    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; Mar 18th 2012 at 04:19 AM.
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