Solve the Differential Equation Using the Method of Variation of Parameters

question 28

Multiple Choice

Solve the differential equation using the method of variation of parameters.
$$y ^ { tt } - y ^ { t } = e ^ { 9 x }$$

• A)
• \(y ( x ) = c _ { 1 } + c _ { 2 } x e ^ { x } + \frac { e ^ { 9 x } } { 72 }\)
• B) \(y ( x ) = c _ { 1 } + x e ^ { 9 x }\)
• C) \(y ( x ) = c _ { 1 } + ( 1 + x ) x e ^ { 9 x }\)
• D) \(y ( x ) = c _ { 1 } + c _ { 2 } e ^ { x } + \frac { e ^ { 9 x } } { 72 }\)
• E) \(y ( x ) = c _ { 1 } + c _ { 2 } x e ^ { 9 x }\)

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Definitions:

Extreme Scores

Statistical outliers in a data set that are significantly higher or lower than most of the data.

Variability

The degree to which data points in a dataset differ from each other and from their mean, indicating the dispersion or spread.

Scores

Quantitative values or measurements used to evaluate or assess someone or something's performance or status.

Negatively Skewed

A distribution of data where most values cluster at the high end with a tail extending to the low end, indicating that the median is greater than the mean.