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. $$y ^ { tt } - 4 y ^ {t } + 3 y = 2 \sin x$$

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

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Definitions:

Holistic Anthropological Perspective

An approach in anthropology that considers the totality of human life, culture, and society in understanding individuals and communities.

Biological And Cultural Homologies

Similarities in biological structures or cultural practices that are inherited from a common ancestor.

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The anthropological study of genes and genetic relationships, which contributes significantly to our understanding of human evolution, adaptation, and diversity.