Solve the Differential Equation $$y ^ { tt } - 8 y ^ { t } + 32 y = 0$$

question 2

Multiple Choice

Solve the differential equation.
$$y ^ { tt } - 8 y ^ { t } + 32 y = 0$$

• A) \(y = e ^ { 4 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } x \sin ( 4 x ) \right)\)
• B) \(y = c _ { 1 } \cos ( 4 x ) + c _ { 2 } x \sin ( 4 x )\)
• C) \(y = e ^ { 4 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } \sin ( 4 x ) \right)\)
• D) \(y = c e ^ { 4 x } \cos ( 4 x )\)

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Definitions:

Atomic Singular Statement

A statement that refers to a specific individual or instance and attributes a property to it, not susceptible to further logical decomposition.

Truth-functional

Relating to the principles of logic, refers to propositional logic where the truth value of a compound sentence is determined by the truth values of its component parts.

Compound

Compound pertains to a substance made up of two or more elements chemically combined in fixed proportions.

Quantifier

In logic and mathematics, a term that specifies the quantity or numerical scope of individuals that a proposition applies to.