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Math Help - First Order ODE

  1. #1
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    First Order ODE

    I am trying to solve:

    (2*-x*\frac{dy}{dx}) +(\frac{dy}{dx})-{y(x)}-1=0

    and I seem to be missing a step: when I solve this i get y = 1 which doesn't seem right.

    Thank you for your help
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  2. #2
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    This can be re-written as \displaystyle \frac{dy}{dx}(1-2x)=y+1 which is separable.

    It becomes \displaystyle \frac{dy}{y+1}= \frac{dx}{1-2x}
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  3. #3
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    It's also first order linear if written as

    \displaystyle \frac{dy}{dx} + \frac{1}{2x - 1}\,y = -\frac{1}{2x-1}

    and so you can use the Integrating Factor Method...
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