Solve the Differential Equation Using the Method of Variation of Parameters

question 147

Multiple Choice

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

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

Understand the dynamic components of love and their significance in interpersonal relationships.

Identify factors that predict attraction and mate selection in adulthood.

Comprehend the differences in mate selection preferences between genders.

Analyze the role of social settings and demographics in the formation and sustainability of various types of relationships.

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Definitions:

Moral

Being related to principles of right and wrong behavior, moral often refers to the ethical judgments and actions considered acceptable by a society or individual.

Ethical

Relating to moral principles or the branch of knowledge dealing with these, often guiding conduct in personal and professional contexts.

Personality

The combination of characteristics or qualities that form an individual's distinctive character, influencing behaviors, thoughts, and patterns of social interaction.

Pleasure Principle

A concept in psychoanalytic theory that seeks immediate gratification of needs and desires without consideration for the moral or societal constraints.