Can Second Order Non-linear ODEs Like This Be Solved Analytically?

[ayae]

Hello, I was wondering if anyone could shed some light upon solving this:

s(x)'' = (a b s(x)) / ||s(x)||^3

Where s is a n dimensional vector, || || is operation finding the magnitude and a and b are constants.

Is this solveable or will I have to use alternative numerical methods?

 

[Lord Crc]

From what I can see, this a second order non-homogeneous ODE, that is it is linear, unless s(x) depends on y(x) in some way.

 

[ayae]

From what I can see, this a second order non-homogeneous ODE, that is it is linear, unless s(x) depends on y(x) in some way.

Damn, silly me. Fixed.

 

[ayae]

bump, I only need it solved in 1, 2 or 3 dimensions.
Anyone please?