Standard +0.8 This is a standard Further Maths FP2 second-order linear differential equation with constant coefficients and a non-homogeneous term. It requires finding the complementary function (complex roots), particular integral (exponential form), then applying initial conditions to find constants. While methodical, it's more demanding than typical A-level questions due to the Further Maths content and multi-step nature, placing it moderately above average difficulty.
8. (a) Find the general solution of the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} t ^ { 2 } } + 2 \frac { \mathrm {~d} y } { \mathrm {~d} t } + 2 y = 2 \mathrm { e } ^ { - t }$$
(b) Find the particular solution that satisfies \(y = 1\) and \(\frac { \mathrm { d } y } { \mathrm {~d} t } = 1\) at \(t = 0\).
(6)(Total 12 marks)