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

question 19

Multiple Choice

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

• A) \(y = \frac { t ^ { 3 } } { 6 } - \frac { 16 } { 7 } t ^ { - 3 } , t > 0\)
• B) \(y = \frac { t ^ { 3 } } { 6 } + \frac { 8 } { 3 } t ^ { - 3 } , t > 0\)
• C) \(y = \frac { t ^ { 3 } } { 6 } + \frac { 32 } { 3 } t ^ { - 3 } , t > 0\)
• D) \(y = \frac { t ^ { 3 } } { 6 } - \frac { 8 } { 3 } t ^ { - 3 } , t > 0\)

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Definitions:

Cash Basis

An accounting method where revenues and expenses are recorded when they are actually received or paid out in cash.

IRR

The Internal Rate of Return is a financial measurement tool used to assess the profitability of prospective investments.

Accounting Basis

The method used to record financial transactions; common methods include cash basis and accrual basis accounting.

Scenario Analysis

A method of evaluating potential future scenarios by contemplating various possible results, often used for strategic planning purposes.