# Math Help - Reduction to first order

1. ## 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

2. Originally Posted by ntfabolous
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.