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Math Help - Separable Partial ODE

  1. #1
    BSc
    BSc is offline
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    Separable Partial ODE

    Find the general solution of:

    x.du/dx - (1/2).y.du/dy=0

    I know that for it to be separable u(x,y)=X(x)Y(y)

    so:

    x.Y(y)dX/dx + (1/2).X(x)dY/dy = 0

    which cancels to:

    x/X(x).(dX/dx) = - y/2Y(y).dY/dy

    so:

    X(x) = -c. Y(y) c is some constant

    so:

    x/X(x).dX/dx = c
    y/2Y(y).dY/dy=c

    from here i am stuck. Any help appreciated
    Thanks
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  2. #2
    Flow Master
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    Quote Originally Posted by BSc View Post
    Find the general solution of:

    x.du/dx - (1/2).y.du/dy=0

    I know that for it to be separable u(x,y)=X(x)Y(y)

    so:

    x.Y(y)dX/dx + (1/2).X(x)dY/dy = 0

    which cancels to:

    x/X(x).(dX/dx) = - y/2Y(y).dY/dy

    so:

    X(x) = -c. Y(y) c is some constant

    so:

    x/X(x).dX/dx = c
    y/2Y(y).dY/dy=c

    from here i am stuck. Any help appreciated
    Thanks
    The two ordinary DE's can be re-arranged into a form where the relevance of Integrating factor - Wikipedia, the free encyclopedia should be obvious.

    Do you need to worry about whether c is positive, negative or zero ......?
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