Solve the Differential Equation $y ^ { \prime } = x e ^ { - \sin x } - y \cos x$

Solve the differential equation. $y ^ { \prime } = x e ^ { - \sin x } - y \cos x$

A) $y = \left( \frac { 1 } { 2 } x ^ { 2 } + C \right) e ^ { - \sin x }$
B) $y = \frac { 1 } { 2 } x + C e ^ { - \cos x }$
C) $y = C e ^ { - \sin x }$
D) $y = e ^ { - \sin x } + C x$
E) $y = \left( 2 x ^ { 2 } + C \right) e ^ { - x } \sin x$

Correct Answer:

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