Find the differential equation for the inductor current ilt

Question

The switch in Figure P9-46 has been open for a long time and is closed at t = 0. The circuit parameters are R = 10 kΩ, L = 100 mH, and V_A = 24 V.

(a) Find the differential equation for the inductor current i_L(t) and initial condition i_L(0).

(b) Transform the equation into the s domain.

(c) Solve the equation for I_L(s).

(d) Take the inverse transform of I_L(s) to find i_L(t).