What do you need to do to it?

I'm a little rusty on diffEQ (what I've had of them, anyway), but don't you need to integrate both sides? In this case, you'd have to do it twice.

I've also not had multivariable calculus, so I'd need to separate the variables.

So, solving for x, we find that

x = -y′ / (y″ - my)

Integrating both sides gives:

1/2 x² + C = ∫[ -y′ / (y″ - my) ]

The integral on the right evades me. Sorry.