Solve the Initial-Value Problem $$r ^ { t } + 2 t r = r , \quad r ( 0 ) = 2$$

Multiple Choice

Solve the initial-value problem. Select the correct answer.
$$r ^ { t } + 2 t r = r , \quad r ( 0 ) = 2$$

A) $r ( t ) = 2 e ^ { t - t ^ { 2 } }$
B) $r ( t ) = 2 e ^ { t - 2 t }$
C) $r ( t ) = e ^ { t - 2 t ^ { 2 } }$
D) $r ( t ) = \frac { e ^ { t ^ { 2 } } } { 2 }$
E) $r ( t ) = 2 e ^ { 2 t }$