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Math Help - Reduction to first order

  1. #1
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    Reduction to first order

    I found this problem pretty difficult... if anyone could find a method to solving it, it would be great for me in class tomorrow.

    Reduce to first order and solve:

    y'' + (1+y^-1)*(y')^2=0



    thanks
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  2. #2
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    Quote Originally Posted by ntfabolous View Post
    I found this problem pretty difficult... if anyone could find a method to solving it, it would be great for me in class tomorrow.

    Reduce to first order and solve:

    y'' + (1+y^-1)*(y')^2=0



    thanks
    First make the sub y'=u

    Now take the derivative with respect to x to get

    \frac{d}{dx}y'=\frac{d}{dx}u

    y''=\frac{du}{dy}\frac{dy}{dx} by the chain rule

    and note that \frac{dy}{dx}=y'=u so we get

    y''=u\frac{du}{dy} so subbing both of these into the equation we get

    u\frac{du}{dy}+(1+y^{-1})u^2=0

    \frac{du}{u}=-(1+y^{-1})dy

    This should get you started good luck.
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