Solve the Differential Equation Using the Method of Variation of Parameters

Multiple Choice

Solve the differential equation using the method of variation of parameters.
$$y ^ {tt } - 4 y ^ { t } + 3 y = 4 \sin x$$
Select the correct answer.

A) $y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 4 } { 5 } \sin x$
B)
$y ( x ) = c _ { 1 } \sin 3 x + \frac { c _ { 2 } } { 4 } x + \cos 3 x$
C)
$y ( x ) = c _ { 1 } \sin x + \frac { c _ { 2 } } { 5 } x + \frac { 2 } { 5 } \sin x$
D)
$y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 4 } { 5 } \cos x + \frac { 2 } { 5 } \sin x$
E)
$y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 2 } { 5 } \sin x$