Solve the Differential Equation Using the Method of Variation of Parameters

question 53

Multiple Choice

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

• 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) \(y ( x ) = \left( c _ { 1 } + x \right) \sin x + \left[ c _ { 2 } + \ln ( \cos x ) \right] \cos x\)

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