Help The charge q on the capacitor in a simple RLC circuit is governed by the equation La" (!) + Ra'() + a 9() = E(), where L is the inductance, R the resistance, C the capacitance, and Ethe voltage source. Since the resistance of a resistor increases with temperature, assume that the resistor is heated so that the resistance at time t is R(t) = 2 + t92. If L = 0.1 H, C = 5 F, E(t)=0, q(0) = 5 C, and q' (0) = 0 A, find the first four nonzero terms in a power series expansion about t = 0 for the charge on the capacitor.

The charge q on the capacitor in a simple RLC circuit is 0.1 henrys governed by the equation Lq"(t) + Rq'(t) + q(t) = E(t), where L 5 farads is the inductance, R the resistance, C the capacitance, and E q(0) = 5 coulombs the voltage source. Since the resistance of a resistor increases R(t) = 2 +t ohms q'(0) =0 amps with temperature, assume that the resistor is heated so that the www resistance at time t is R(t) = 2 +t S. If L = 0.1 H, C=5 F, E(t)=0, q(0) =5 C, and q'(0) =0 A, find the first four nonzero terms in a power series expansion about t = 0 for the charge on the capacitor. q(t ) = + ... (Type an expression that includes all terms up to order 4.)