Chapter 8.3, Problem 12E

(a)

To determine

The solution of the system of differential equation $\frac{d}{dt}\left(\begin{array}{l}{i}_2\\ i_3\end{array}\right)=\left(\begin{array}{cc}-\frac{R_1}{L_1}& -\frac{R_1}{L_1}\\ -\frac{R_1}{L_2}& \frac{-\left(R_1+R_2\right)}{L_2}\end{array}\right)\left(\begin{array}{l}{i}_2\\ i_3\end{array}\right)+\left(\begin{array}{l}\frac{E}{L_1}\\ \frac{E}{L_2}\end{array}\right)$ by the method of undetermined coefficients.

(b)

To determine

The value of the current $i_1\left(t\right)$ in the given diagram of the circuit.