Find the particular solution to the initial value problem dy dt - 2ty = = 0 y(0) = 1 y' (0) = 2 For your answer write the first four terms of the solution's series. Suppose a weight of mass 5 kg is attached to a spring with spring constant k = 5 N/m and damping constant c = 10 Ns/m. At t=0 the mass is 0.1 m below its equilibrium position with velocity 0.2 m/s toward the equilibrium position. How many times will the mass return to its equilibrium position? Hint: either never, once, or infinitely many times.