A circuit consists of four components in series: a battery with voltage 150 Volts, a capac- itor with capacitance 0.02 Farads, an inductor with inductance 2 Henry, and a resistor with resistance 16 Ohms. Initially, the charge on the capacitor and the current in the circuit are zero.
(i) Let q(t) Coulombs be the charge on the capacitor at time t seconds. Prove that q satisfies the differential equation
q" + 8q' + 25q = 75

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