QUESTION 1: a) Solve the differential equation (2 + sin z + z*e")dy + (y cos z+ 2re" 62)dx = 0. b) Show that dy ye? dr rei - y is homogeneous. Hence, solve the differential equation. c) An electromotive force, E(t) of 200-volt is applied to an RC series circuit in which the resistance, R is 1000 ohm and the inductance, L is 5 farad. If the differential equation for the current I(t) can be modelled as L+ RI = E(t), IP dt then determine i. the current on the capacitor if given I(0) = 0.4, ii. the current as t oo.