Solve the Differential Equation Using the Method of Variation of Parameters

question 52

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

---

Definitions:

Companionate Love

A form of love characterized by deep affection, emotional closeness, and a strong bond, without necessarily including passion or physical attraction.

Relationship Satisfaction

A measure of joy or contentment individuals feel regarding their interpersonal relationships, including romantic partnerships.

Passionate Love

A state of intense longing for union with another. Passionate love is characterized by strong emotions, sexual desire, and anxiety.

Sternberg

Refers to Robert Sternberg, a psychologist known for his theory on love and intelligence, which includes the triangular theory of love and the triarchic theory of intelligence.