Solve the given differential equations (Q. 32 & Q 35) using both the Integration Factor technique and Laplace Transforms. Explain or show your method of solution. 32. If a circuit contains only an inductance and a resistance, with L = 2.0 H, and R = 30 0, find the current i as a function of time t if the initial current is 0.020A. See figure 31.7 below. [ans.: i = 0.020e->amps] WW Fig. 31.7 35. If a circuit contains only a resistance and capacitance; C, find the equation relating the charge; q, on a the capacitor in terms of the time t if i = - and q = q, (whent = 0), see figure 31.9 below. [ans. : q = q e RC coulombs] Fig. 31.9 R