Solving 2nd Order PDE for dx/ds in d^2x/ds^2 - (2/y)(dx/ds)(dy/ds) = 0

[queequag]

Homework Statement

Need to solve for dx/ds in the following equation, keeping dy/ds.

Homework Equations

d^2x/ds^2 - (2/y)(dx/ds)(dy/ds) = 0

The Attempt at a Solution

I can just rearrange to get:

dx/ds = (y/2)(ds/dy)(d^2x/ds^2)

But, this is not clean to use for some later calculations.

Is there any way to solve for dx/ds by integration?

 

[CompuChip]

Would it help you if I noticed that

$$\frac{d^2x}{ds^2} / \frac{dx}{ds} = \frac{d}{ds} \ln\left( \frac{dx}{ds} \right)$$
?