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

Identify and explain situations where consideration is deemed inadequate or unconscionable.

Comprehend the principles of accord and satisfaction in the context of settling debts.

Understand the application of promissory estoppel in agreement enforcement.

Analyze the impact of preexisting duties on the enforceability of new agreements.

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