Another Dif EQ, yay.

I have to solve the following Dif EQ, and give the interval for which the largest general solution is defined:

dP/dt + 2tP = P + 4t - 2

So I don't think I can do separation of variables, so I tried integrating factors...

P(x) = 2t

M(x) = e^(int(2t)dt) = e^(2t^3/3)

So multiply M(x) to each term:

e^(2t^3/3)*dP/dt + e^(2t^3/3)*2tP = e^(2t^3/3)*P + e^(2t^3/3)*4t - 2*e^(2t^3/3)

So this looks very messy now...

Again, it's the part after this that I get stuck.