The charge q on the capacitor in a simple RLC circuit is governed by the equation 0.2 henrys 1 808080 Lq"(t) + Rq'(t) + q(t)= E(t), where L is the inductance, R the resistance, C the 5 farads capacitance, and E the voltage source. Since the resistance of a resistor q(0) = 4 coulombs R(t) =1+ - ohms increases with temperature, assume that the resistor is heated so that the q'(0) =0 amps resistance at time t is R(t) = 1 + - $ If L =0.2 H, C = 5 F, E(t)=0, q(0) = 4 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.)