Solve the Initial Value Problem $$2 \frac { d y } { d x } - 4 x y = 8 x ; y ( 0 ) = 23$$

question 35

Multiple Choice

Solve the initial value problem.
- $$2 \frac { d y } { d x } - 4 x y = 8 x ; y ( 0 ) = 23$$

• A) \(y = 2 + 23 e ^ { x ^ { 2 } }\)
• B) \(y = - 1 + 24 e ^ { x ^ { 2 } }\)
• C) \(y = - 2 + 25 e ^ { - x ^ { 2 } }\)
• D) \(y = - 2 + 25 \mathrm { e } ^ { 2 }\)

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Definitions:

Correlation

A statistical measure that expresses the extent to which two variables change together, indicating the strength and direction of their relationship.

Probability Distribution

A statistical description enumerating all likely values and their corresponding probabilities for a random variable within a set interval.

Error Variable \(ε\)

In statistical modeling, particularly in linear regression, it represents unobserved random errors or deviations of observed values from their expected values.

Scatter Diagram

A graphical representation that shows the relationship between two quantitative variables by plotting data points on a two-dimensional plane.