Chapter 4.1, Problem 8E

In Problems 7–9, find a synchronous solution of the form A $A\cos \Omega t+B\sin \Omega t$ to the given forced oscillator equation using the method of Example 4 to solve for $\text{A}$ and $\text{B}$.

$y^{″}+2y^{\prime }+5y=-50\sin 5t$, $\Omega =5$.