The initial-value problem that governs the behavior of a coupled spring-mass system is (see the introduction to this chapter)
$$
\begin{aligned}
m_{1} \frac{d^{2} x}{d t^{2}} &=-k_{1} x+k_{2}(y-x) \\
m_{2} \frac{d^{2} y}{d t^{2}} &=-k_{2}(y-x) \\
x(0)=\alpha_{1}, & x^{\prime}(0)=\alpha_{2}, \quad y(0)=\alpha_{3}, \quad y^{\prime}(0)=\alpha_{4}
\end{aligned}
$$
where $\alpha_{1}, \alpha_{2}, \alpha_{3},$ and $\alpha_{4}$ are constants. Convert this problem into an initial-value problem for an equivalent first-order linear system. (You must give the appropriate initial conditions in the new variables.)