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Math Help - first order ODE

  1. #1
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    first order ODE

    I would like to solve the differential equation
    (x+y-1)dx +(y-x-5)dy = 0
    This is not exact. I really cannot figure out the answer.
    Anyone can help? thanks in advance.
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  2. #2
    MHF Contributor

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    Quote Originally Posted by tszhin8831 View Post
    I would like to solve the differential equation
    (x+y-1)dx +(y-x-5)dy = 0
    This is not exact. I really cannot figure out the answer.
    Anyone can help? thanks in advance.
    first solve the system of equations: x + y = 1, y - x = 5, to get x = -2, y = 3. now let u = x + 2 and v = y - 3. then your equation becomes: (v + u)du + (v - u)dv = 0, which is homogeneous.
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