4. $$y = 3 \mathrm { e } ^ { - x } \cos 3 x + A \mathrm { e } ^ { - x } \sin 3 x$$ is a particular integral of the differential equation $$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } - 2 \frac { \mathrm {~d} y } { \mathrm {~d} x } + 10 y = 40 \mathrm { e } ^ { - x } \sin 3 x$$ where \(A\) is a constant.

1. Find the value of \(A\).
2. Hence find the general solution of this differential equation.
3. Find the particular solution of this differential equation for which both \(y = 3\) and \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 3\) at \(x = 0\)