Chapter 25, Problem 18P

The following is an initial value, second-order differential equation:

$\begin{array}{l}\frac{d^{2}y}{d{t}^2}+\left(5x\right)\frac{dx}{dt}+\left(x+7\right)\sin \left(\omega t\right)=0\\ \text{where}\\ \frac{dx}{dt}\left(0\right)=1.5\text{ and }x\left(0\right)=6\end{array}$ $\omega =1$

Note that $\omega =1$. Decompose the equation into two first-order differential equations. After the decomposition, solve the system from $t=0\text{ to 15}$ and plot the results.