8.2.2.12 Systems of differential equations

condition: Find a particular solution to the system of differential equations that satisfies the specified initial conditions. Solve the system using the operational calculus method. \[ \left\{\begin{array}{l} \frac{d x}{d t}+\frac{d y}{d t}+4 y+4 x=0 \\ \frac{d x}{d t}+5 \frac{d y}{d t}+28 y=0 \end{array}, \quad x(0)=1, \quad y(0)=2\right. \]