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:

Fixed Costs

Regularly occurring costs that remain constant in total, irrespective of changes in operational levels or volume of output.

Variable Costs

Costs that change in direct proportion with the level of output or activity of a business.

Underapplied Overhead

occurs when the allocated manufacturing overhead cost is less than the actual overhead incurred, leading to a discrepancy.

Overapplied Overhead

A situation where the allocated manufacturing overhead costs exceed the actual overhead costs incurred.