In solving a problem involving differential equations, I come across the following:
$\ddot{y} + 4\omega^2y = 2\omega gt\sin{\lambda} \equiv ct$
The general solution is the general solution of the homogeneous equation and one particular solution of the inhomogeneous equation, i.e.,
$y = \frac{c}{4\omega^2}t + A\sin{2\omega t} + B\cos{2\omega t}$
I'm at a loss as to how it got to $y$. I can only think of the following:
$\dot y + 4\omega^2yt = \omega gt^2\sin{\lambda} + C$
which of course is nowhere near what I read. I'd appreciate if someone can point me in the right direction.