2. At time \(t\) seconds, the position vector of a particle \(P\) is \(\mathbf { r }\) metres, where \(\mathbf { r }\) satisfies the vector differential equation $$\frac { \mathrm { d } ^ { 2 } \mathbf { r } } { \mathrm {~d} t ^ { 2 } } + 4 \mathbf { r } = \mathrm { e } ^ { 2 t } \mathbf { j }$$ When \(t = 0 , P\) has position vector \(( \mathbf { i } + \mathbf { j } ) \mathrm { m }\) and velocity \(2 \mathbf { i } \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find an expression for \(\mathbf { r }\) in terms of \(t\).