Solve the Initial Value Problem $$t \frac { d y } { d t } + 4 y = t ^ { 3 } ; t > 0 , y ( 2 ) = 1$$

question 76

Multiple Choice

Solve the initial value problem.
- $$t \frac { d y } { d t } + 4 y = t ^ { 3 } ; t > 0 , y ( 2 ) = 1$$

• A) \(y = \frac { t ^ { 3 } } { 7 } + \frac { 144 } { 7 } t ^ { - 4 } , t > 0\)
• B) \(y = \frac { t ^ { 3 } } { 7 } - \frac { 16 } { 7 } t ^ { - 4 } , t > 0\)
• C) \(y = \frac { t ^ { 3 } } { 7 } - 2 t ^ { - 4 } , t > 0\)
• D) \(y = \frac { t ^ { 3 } } { 7 } + \frac { 16 } { 7 } t ^ { - 4 } , t > 0\)

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Definitions:

Regression Toward

A psychological defense mechanism involving a return to an earlier stage of development when faced with stress.

Mean

The arithmetic average of a set of numbers, obtained by adding them together and dividing by the count of those numbers.

Correlation Coefficients

Statistical measures that describe the strength and direction of the relationship between two variables.

Relationship

refers to a connection, association, or involvement between two or more individuals, groups, or entities.