Solve the Differential Equation $$y ^ { tt } - 4 y ^ { t } + 13 y = 0$$

question 131

Multiple Choice

Solve the differential equation. Select the correct answer.
$$y ^ { tt } - 4 y ^ { t } + 13 y = 0$$

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

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Definitions:

Nature Versus Nurture

A debate concerning the relative importance of an individual's innate qualities ("nature") versus personal experiences ("nurture") in determining or causing differences in physical and behavioral traits.

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Heredity is the passing on of physical or mental characteristics genetically from one generation to another.

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The surrounding conditions or influences that affect the growth, development, and survival of organisms, including humans.

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