I hope there is a detailed process. thank you ????

The circuit shown in Figure Q3 contains resistor, inductor and capacitor components. The ODE of the circuit is $L I^{''} + R I^{'} + \frac{1}{c} I = E^{'} (t)$ . Assuming $R = 4Ω, L = 0.1 H, C = 0.025 F, E =$ $10 sin 10 t V$ , the initial current and charge are zero. Figure Q3 (a) Find the general solution for the homogeneous part of the ODE. (b) Solve the ODE by considering the initial conditions.

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I hope there is a detailed process. thank you ????

The circuit shown in Figure Q3 contains resistor, inductor and capacitor components. The ODE of the circuit is

L I^{''} + R I^{'} + \frac{1}{c} I = E^{'} (t)

. Assuming

R = 4Ω, L = 0.1 H, C = 0.025 F, E =

10 sin 10 t V

, the initial current and charge are zero. Figure Q3 (a) Find the general solution for the homogeneous part of the ODE. (b) Solve the ODE by considering the initial conditions.

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