Solve the Differential Equation Using the Method of Variation of Parameters

Multiple Choice

Solve the differential equation using the method of variation of parameters. $y ^ { \prime \prime } - 4 y ^ { \prime } + 3 y = 2 \sin x$

A) $y ( x ) = c _ { 1 } \sin x + \frac { c _ { 2 } } { 5 } x + \frac { 2 } { 10 } \sin x$
B) $y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 2 } { 5 } \sin x$
C) $y ( x ) = c _ { 1 } \sin 3 x + \frac { c _ { 2 } } { 4 } x + \cos 3 x$
D) $y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 2 } { 10 } \sin x$
E) $y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 2 } { 5 } \cos x + \frac { 2 } { 10 } \sin x$