Chapter 7, Problem 138RE

The following problems consider the “beats” that occur when the forcing term of a differential equation causes “slow" and “fast” amplitudes. Consider the general differential equation $a{y}^{″}+by=\cos \left(\omega t\right)$ that governs undamped motion. Assume that $\sqrt{\frac{b}{a}\ne }\omega$ .

138. Find the general solution to this equation (Hint: call ${\omega }_0=\sqrt{b/a}$ ).