- Solve the differential equation
$$\frac { \mathrm { d } \mathbf { r } } { \mathrm {~d} t } - 2 \mathbf { r } = \mathbf { 0 }$$
given that when \(t = 0 , \mathbf { r } . \mathbf { j } = 0\) and \(\mathbf { r } \times \mathbf { j } = \mathbf { i } + \mathbf { k }\).