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Math Help - First-order nonlinear ordinary differential equation

  1. #1
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    First-order nonlinear ordinary differential equation

    How do I solve this one?

    (2x - y + 4)dy + (x - 2y + 5)dx = 0
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: First-order nonlinear ordinary differential equation

    Quote Originally Posted by mafra View Post
    How do I solve this one?

    (2x - y + 4)dy + (x - 2y + 5)dx = 0
    \frac{dy}{dx}=\frac{2y-x-5}{2x-y+4}

    Let x=u+h and y=v+h, where h and k are constants that are to be determined.

    dx=du and dy=dv

    We want \frac{dv}{du}=\frac{2v-u}{2u-v}, so that we have a homogeneous equation, that can be easily solved.

    Find h and k by setting 2y-x-5=2v-u and 2x-y+4=2u-v+4.
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