$y′′ + b^2{y} = f(t)$
$ f(t) = t$ for $0 < t < 2\pi$ ($2\pi$ periodic sawtooth wave)
This is my solution to the differential equation.
$y(t) = C_1\cos(bt) + C_2\sin(bt) + b^{-3}\left(bt - \sin(bt)\right) - 2\pi b^{-2}* \sum\limits_{n=1}^{\infty} (1 - \cos\left(bt - 2\pi an)\right)u(t - 2\pi n)$
$C_1$, $C_2$ are constants, $b$ is positive real number and $u$ is unit step function. I need to find for which values of $b$ does this equation above have a bounded solution. I have no idea how to solve this problem. Any help would be greatly appreciated.