3. (5%) Determine the existence and uniqueness of the solutions to the system

(b) (5%) Obtain the "steady-state" current in the RLC-circuit when R=50 Ω (Ohm),L = 30 H (Henry), C = 0.025 F (Farad), and E = 200 sin(4t) V (Volt)Hint: The voltage drop for a current i(t) across a resistor of resistance R is Ri(t), across an inductor of inductance L is L, and across a capacitor of capacitance C is Q/C, where Q is the charge and the relation between Q(t) and i(t) is Q(t) = ∫ i(t)dt

3. (5%) Determine the existence and uniqueness of the solutions to the system

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