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:

Profit Maximization

The approach a business takes to determine the pricing and output that lead to the utmost profit.

Production Function

Describes the technological relationship between the quantity of inputs used and the quantity of output produced.

Production Function

An equation that describes the maximum amount of output that can be produced with a given set of inputs.

Profit Maximization

A strategy employed by businesses to find the price and production levels that maximize profits.