Find $\vec { r } ( t ) = \langle x ( t ) , y ( t ) \rangle$

Essay

Find $\vec { r } ( t ) = \langle x ( t ) , y ( t ) \rangle$ determined by $\begin{array} { l } x ^ { \prime } ( t ) = x ( t ) , y ^ { \prime } ( t ) = t \\x ( 0 ) = 1 , y ( 0 ) = 1\end{array}$