- (a) Find the general solution of the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 2 \frac { \mathrm {~d} y } { \mathrm {~d} x } + 10 y = 27 \mathrm { e } ^ { - x }$$
(b) Find the particular solution that satisfies \(y = 0\) and \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\) when \(x = 0\)