Differential Equations - separable?

[pian0forte]

Homework Statement

Find the general solution, y

2ty dy/dt = 3y^2 - t^2

Homework Equations

The Attempt at a Solution

I probably have to separate the equation and get y's one side in order to solve, but I'm stuck as to how to separate it. I tried letting u = y/t, so then

du/dt = (t dy/dt - y)/(t^2)
then dy/dt = t du/dt + u , so I plugged it back into the equation?

t du/dt + u = (3y^2 - t^2)/(2ty)
t du/dt + u = (3/2)u - (1/2u)

I can separate this into:
(u/(u^2-1)) du/dt = 1/2t

Am I on the right track?

 

[Dr.D]

Looks like your last line separates to
(u/(u^2-1))du = dt/(2t)