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

ayae
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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?
 
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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.
 
Lord Crc said:
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.
 
bump, I only need it solved in 1, 2 or 3 dimensions.
Anyone please?
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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