First off, this is and ODE since there are only ordinary derivatives here. If you write your ODE as
You can integrate giving
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)