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Thread: PDE

  1. #1
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    PDE

    $\displaystyle
    u(x,y) = B (3x - 2y)
    $

    B is an arbitary function

    find partial differentiation of u. Not including B
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  2. #2
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    Quote Originally Posted by harveyo View Post
    $\displaystyle
    u(x,y) = B (3x - 2y)
    $

    B is an arbitary function

    find partial differentiation of u. Not including B
    $\displaystyle \frac{\partial u}{\partial x} = 3B$ .... (1)

    $\displaystyle \frac{\partial u}{\partial y} = -2B$ .... (2)

    At this level you should be able to combine these two equations in such a way as to eliminate B.
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  3. #3
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    i had

    $\displaystyle
    dy/dx = \partial x / \partial y = 3B (3x-2y)/ 2B (3x-2y) = -3/2
    $

    was this right?
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  4. #4
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    Quote Originally Posted by harveyo View Post
    i had

    $\displaystyle
    dy/dx = \partial x / \partial y = 3B (3x-2y)/ 2B (3x-2y) = -3/2
    $

    was this right?
    i have used the wrong formula here?

    i should solve the above simultaneously?
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    $\displaystyle \frac{\partial u}{\partial x} = 3B$ .... (1)

    $\displaystyle \frac{\partial u}{\partial y} = -2B$ .... (2)

    At this level you should be able to combine these two equations in such a way as to eliminate B.
    $\displaystyle 2\frac{\partial u}{\partial x} = 6B$ .... (1)

    $\displaystyle 3\frac{\partial u}{\partial y} = -6B$ .... (2)

    hence

    $\displaystyle 2\frac{\partial u}{\partial x} + 3\frac{\partial u}{\partial y} = 0 $
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