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)
• \(y ( x ) = c _ { 1 } e ^ { 3 x } + c _ { 2 } e ^ { x } + \frac { 2 } { 5 } \sin x\)

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Definitions:

Unit Price Elastic

A situation in which the percentage change in quantity demanded is equal to the percentage change in price, resulting in no change in total revenue.

Total Revenue

The total revenue a company earns from selling its goods or services before deducting any expenses or costs.

Chocolate

A sweet, usually brown, food preparation of roasted and ground cacao seeds, often flavored, and available as a solid or liquid.

Unit Elastic

A situation in which the quantity demanded or supplied changes by an equal percentage as the change in price.