Solve the Differential Equation Using the Method of Variation of Parameters

question 61

Multiple Choice

Solve the differential equation using the method of variation of parameters.
Select the correct answer.
$$y ^ { tt } - y ^ { t } = e ^ { 2 x }$$

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

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Definitions:

Marginal Change

A small incremental adjustment to a plan of action.

Incremental Adjustment

Small, gradual changes or modifications made in response to changing conditions or to improve a process or system.

Scarcity

A fundamental economic problem of having seemingly limitless human wants in a world of limited resources, leading to the necessity of making trade-offs.

Marginal Cost

Marginal cost is the cost of producing one more unit of a good or service, which can vary depending on the level of production.