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Math Help - First order ODE

  1. #1
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    First order ODE

    xy' + y - 2x = 0

    We need to learn the method where you re-arrange too

    N(x,y)dy + M(x,y)dx = 0

    Then solve somehow getting d(y-2x)/dy = 1 etc...

    Sorry I do not know the name of this method, but I really could do with a step by step sort of guide on how to do it for any example, as I can solve this in many other ways, but don't understand this particular method of solving 1st Order ODE's

    Thanks.
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  2. #2
    A Plied Mathematician
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    I think you're talking about exact equations. See Chris's tutorial, post # 2 (scroll down a little bit).
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  3. #3
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    I think you're right, thanks for the help.
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  4. #4
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    An alternative:

    \displaystyle x\,\frac{dy}{dx} + y - 2x = 0

    \displaystyle x\,\frac{dy}{dx} + y = 2x

    \displaystyle \frac{d}{dx}(x\,y) = 2x

    \displaystyle x\,y = \int{2x\,dx}

    \displaystyle x\,y = x^2 + C

    \displaystyle y = x + \frac{C}{x}.
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  5. #5
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    Thanks for trying with the help prove it, I already have the Integrating Factor, Seperation of Variables and also the (y=uv) Method, just needed to learn this one for the course incase it appears on the exam

    Thanks anyway tho, brilliant sig btw ! lol
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