I'm trying to figure out how to do this problem and we've just covered bernoulli equations in class so I know I have to use that. This is the problem:

Solve the equation

$\displaystyle y' = (X cos(t) + T)y - y^3$

where X and T are constants.

So far I have this:

$\displaystyle dy/dt - (X cos(t) + T)y = -y^3$

then using integrating factor:

$\displaystyle e^\int(Xcos(t) + T)) = e^(Xsin(t) + Tt + C) = e^(Tt)* e^(xsin(t)) * e^C$

But where do I go from here?