Chapter 8.3, Problem 12E

1. (a) The system of differential equations for the currents i₂(t) and i₃(t) in the electrical network shown in Figure 8.3.2 is

   $\frac{d}{dt}\left(\begin{array}{c}{i}_2\\ i_3\end{array}\right)=\left(\begin{array}{cc}-R_1/L_1& -R_1/L_1\\ -R_1/L_2& -(R_1/R_2)L_2\end{array}\right)\left(\begin{array}{c}{i}_2\\ i_3\end{array}\right)+\left(\begin{array}{c}E/L_1\\ E/L_2\end{array}\right).$

   Use the method of undetermined coefficients to solve the system if R₁ = 2 Ω, R₂ = 3 Ω, L₁ = 1 h, L₂ = 1 h, E = 60 V, i₂(0) = 0, and i₃(0) = 0.

2. (b) Determine the current i₁(t).