Find the differential equation for the inductor current ilt, Physics

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Find the differential equation for the inductor current ilt

The switch in Figure P9-46 has been closed for a long time and is opened at t = 0. The circuit parameters are R = 50 Ω, L = 200 mH, and V_A = 30 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.

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

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