5 It is given that \(y\) satisfies the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 3 \frac { \mathrm {~d} y } { \mathrm {~d} x } + 2 y = 2 \mathrm { e } ^ { - 2 x }$$
- Find the value of the constant \(p\) for which \(y = p x \mathrm { e } ^ { - 2 x }\) is a particular integral of the given differential equation.
- Solve the differential equation, expressing \(y\) in terms of \(x\), given that \(y = 2\) and \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\) when \(x = 0\).