Solve the Differential Equation Using the Method of Variation of Parameters

Multiple Choice

Solve the differential equation using the method of variation of parameters. $y ^ { \prime \prime } + y = \sec x , \frac { \pi } { 4 } < x < \frac { \pi } { 2 }$

A) $y ( x ) = c _ { 1 } + \left[ c _ { 2 } + \ln ( \sin x ) \right] \sin x$
B) $y ( x ) = \left( c _ { 1 } + x \right) \sin x + c _ { 2 } + \ln ( \cos x )$
C) $y ( x ) = \frac { \pi } { 2 } \sin x + \left[ \frac { \pi } { 2 } + \ln ( \cos x ) \right] \cos x$
D) $y ( x ) = \left[ \frac { \pi } { 4 } + \ln ( \cos x ) \right] \cos x$
E) $y ( x ) = \left( c _ { 1 } + x \right) \sin x + \left[ c _ { 2 } + \ln ( \cos x ) \right] \cos x$