Solve the Initial Value Problem $$\frac { d ^ { 2 } y } { d x ^ { 2 } } = 5 - 3 x , y ^ { \prime } ( 0 ) = 8 , y ( 0 ) = 2$$

question 126

Multiple Choice

Solve the initial value problem.
- $$\frac { d ^ { 2 } y } { d x ^ { 2 } } = 5 - 3 x , y ^ { \prime } ( 0 ) = 8 , y ( 0 ) = 2$$

• A) \(y = 5 x ^ { 2 } + 3 x ^ { 3 } + 8 x + 2\)
• B) \(y = \frac { 5 } { 2 } x ^ { 2 } + \frac { 1 } { 2 } x ^ { 3 } - 8 x - 2\)
• C) \(\mathrm { y } = 2\)
• D) \(y = \frac { 5 } { 2 } x ^ { 2 } - \frac { 1 } { 2 } x ^ { 3 } + 8 x + 2\)

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Definitions:

Simultaneously

Simultaneously means occurring, operating, or done at the same time.

Inverse Relationship

A relationship between two variables in which an increase in the value of one variable leads to a decrease in the value of the other variable, and vice versa.

Type I Error

The mistaken dismissal of a correct null hypothesis, referred to as a "false positive."

Type II Error

A statistical mistake made by failing to reject a false null hypothesis, also known as a false negative.