Chapter 5.7, Problem 21E

[M] Find formulas for the current it and the voltage v_c for the circuit in Example 3, assuming that R₁ = 1 ohm, R₂ = .125 ohm. C = .2 farad. L = .125 henry, the initial current is 0 amp, and the initial voltage is 15 volts.

EXAMPLE 3 The circuit in Figure 4 can be described by the equation

$\left[\begin{array}{c}{i^{\prime }}_L(t)\\ {v^{\prime }}_{{}_C}\end{array}\right]=\left[\begin{array}{cc}-R_2/L& -1/L\\ 1/C& -1/(R_{1}C)\end{array}\right]\left[\begin{array}{c}\begin{array}{c}{i}_L\\ v_C\end{array}\end{array}\right]$