Chapter 1.2, Problem 30P

Verify that the function in Eq.(11) is a solution of Eq. (10).

Eq. (10): $\frac{du}{dt}+ku=k{T}_0+kA\sin \omega t$.

Eq. (11): $u=T_0+\frac{kA}{k^2+{\omega }^2}\left(k\sin \omega t-\omega \cos \omega t\right)+c{e}^{-kt}$.