- A particle \(P\) moves in a plane such that its position vector \(\mathbf { r }\) metres at time \(t\) seconds \(( t > 0 )\) satisfies the differential equation
$$\frac { \mathrm { d } \mathbf { r } } { \mathrm {~d} t } - \frac { 2 } { t } \mathbf { r } = 4 \mathbf { i }$$
When \(t = 1\), the particle is at the point with position vector \(( \mathbf { i } + \mathbf { j } ) \mathrm { m }\).
Find \(\mathbf { r }\) in terms of \(t\).