1. Suppose a homogeneous second order differential equation has fundamental pair {t, t³}. Solve the IVP with y(2) = 1 and y'(2) = -3. 2. A 0.2kg weight stretches a spring 0.1m. The system is submerged in oil with damping coefficient Y = 3. The weight is then lowered by 0.2m and released with a downward velocity of 1m/s. There is no external force. (a) Find the spring coefficient k. (b) Write down but do not solve the initial value problem corresponding to this situation. (c) Is this system underdamped, critically damped or overdamped? Show the associated calculation. (d) Sketch a reasonable graph of the solution. 3. Write down the general solution to the differential equation D³y + 4D³y = 0.