Find the circuit integrodifferential equation that, Electrical Engineering

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Find the circuit integrodifferential equation that

The RLC circuit in Figure is in the zero state when at t = 0 an exponential source, v_S(t) = V_Ae^-αt V, is suddenly connected to it.

497_Figure 2.jpg

(a) Find the circuit integrodifferential equation that describes the behavior of the current in the circuit.

(b) If R = 82 Ω, L = 100 mH, C = 15 μF, V_A = 15 V, and α = 500 s-1, use Laplace transforms and MATLAB to solve for i(t) for t ≥ 0:

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