You do not need to nd the coe cients! Y (t) = y1(t) + y2(t) + y3(t) where. Y1(t) = a1t cos t + b1t sin t + c1 cos t + d1 sin t. Y3(t) = a3t2 + b3t + c3 : solve the following initial value problem: y (t) + 3y + 2y = 4et, y(0) = 0, y (0) = 1 . y(t) = Initial position and velocity respectively are: x(0) = 3cm, x (0) = 1cm. (a) write down the di erential equation which governs the system. 2x + 4x + 20x = 0 . (b) write down the initial energy of the system. E(0) = 91 kgcm2 s2 (c) show, by using the di erential equation, that the energy is mono- tone nonincreasing. 0 = 2x + 4x + 20x multiplying through by x gives. On the other hand, the energy of this system as a function of time is given by:
