
solving 2nd order PDE
Need to solve for dx/ds in the following equation, keeping dy/ds.
d^2x/ds^2  (2/y)(dx/ds)(dy/ds) = 0
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?I would like an expression with dx/ds = f(y,s)

First off, this is and ODE since there are only ordinary derivatives here. If you write your ODE as
$\displaystyle \dfrac{\dfrac{d^2x}{ds^2}}{\dfrac{d x}{d s} }= 2 \dfrac{\dfrac{dy}{ds}}{y}$
You can integrate giving
$\displaystyle \ln \dfrac{d x}{d s}} = 2 \ln y + \ln c$
or
$\displaystyle \dfrac{dx}{ds} = c y^2$