Solve the Differential Equation Using the Method of Variation of Parameters

Multiple Choice

Solve the differential equation using the method of variation of parameters.
Select the correct answer.
$$y ^ { tt } - y ^ { t } = e ^ { 2 x }$$

A) $y ( x ) = c _ { 1 } + c _ { 2 } e ^ { x } + \frac { e ^ { 2 x } } { 2 }$
B) $y ( x ) = c _ { 1 } + c _ { 2 } x e ^ { 2 x }$
C) $y ( x ) = c _ { 1 } + x e ^ { 2 x }$
D) $y ( x ) = c _ { 1 } + c _ { 2 } x e ^ { x } + \frac { e ^ { 2 x } } { 2 }$
E) $y ( x ) = c _ { 1 } + ( 1 + x ) x e ^ { 2 x }$