Transform these equations into the s domain and solve for

Question

Solving State Variable Equations With zero input, a series RLC circuit can be described by the following coupled first-order equations in the inductor current i_L(t) and capacitor voltage v_C(t).

(a) Transform these equations into the s domain and solve for the transforms I_L(s) and V_C(s) in terms of the initial conditions i_L(0) = I₀ and v_C(0) = V₀.

(b) Find i_L(t) and v_C(t) for R = 100 Ω, L = 100 mH, C = 1 μF, I₀ = 10 mA, and V0 = 15 V.