Q.1 Show that the function y = 1/x + x/2 is a solution of the differential equation dy/dx = 1 - y/x. Q.2 Show that the function y = cos x / x is a solution of the differential equation x(dy/dx) + y = -sin x. Q.3 Solve dy/dx = e^(2x-y) / e^(x+y). Q.4 Solve sqrt(x) dy/dx = e^(y+sqrt(x)). Q.5 Suppose that electricity is draining from a capacitor at a rate that is proportional to the voltage V across its terminals and that, if t is measured in seconds, dV/dt = -1/40 V. Solve this equation for V, using V0 to denote the value of V when t = 0. How long will it take the voltage to drop 10% of its original value?