Solve the Differential Equation Using the Method of Variation of Parameters

question 31

Multiple Choice

Solve the differential equation using the method of variation of parameters. $$y ^ { tt } - 4 y ^ { t } + 3 y = 3 \sin x$$

• A) \(y ( x ) = c _ { 1 } \sin 3 x + \frac { c _ { 2 } } { 4 } x + \cos 3 x\)
• B) \(y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 3 } { 5 } \cos x + \frac { 3 } { 10 } \sin x\)
• C) \(y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 3 } { 5 } \sin x\)
• D) \(y ( x ) = c _ { 1 } \sin x + \frac { c _ { 2 } } { 5 } x + \frac { 3 } { 10 } \sin x\)
• E) \(y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 3 } { 10 } \sin x\)

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Definitions:

Voyeuristic Disorder

Disorder characterized by obtainment of sexual arousal by compulsively and secretly watching another person undressing, bathing, engaging in sex, or being naked.

Exhibitionistic Disorder

A mental condition marked by a compulsion to expose one’s genitals to an unsuspecting person for sexual gratification.

Frotteuristic Disorder

Disorder characterized by obtainment of sexual gratification by rubbing one’s genitals against or fondling the body parts of a nonconsenting person.

Sexual Sadism

A condition where individuals derive pleasure from inflicting pain or humiliation on others.