Find the solution of the differential equation that satisfies the given initial condition. _ xsin(X) _ _ a }" J' y(0) _ 7 When a raindrop fails, it increases in size, and so its mass at time t is a function of t, namely, m(t). The rate of growth of the mass is km(t) for some positive constant k. When we apply Newton's law of motion to the raindrop, we get (mv)' = gm, where v is the velocity of the raindrop (directed downward) and t is the acceleration due to gravity. The terminal velocity of the raindrop is Iim v(t). tam Find an expression for the terminal velocity in terms ofg and k. lim v(t) = tsoc Solve the differential equation xy' = y + xesy/* by making the change of variable v = y/x. 3v X e + 3 In x + C XFind the solution of the differential equation that satisfies the given initial condition. dA = Ab2 cos(br), A(0) = 63 dr