Solve the Initial-Value Problem $\frac { d y } { d t } = \frac { 2 t } { y ^ { 2 } + t ^ { 2 } y ^ { 2 } }$

question 15

Multiple Choice

Solve the initial-value problem $\frac { d y } { d t } = \frac { 2 t } { y ^ { 2 } + t ^ { 2 } y ^ { 2 } }$ , $y ( 0 ) = 3$ . Then use your solution to evaluate $y ( \sqrt { e - 1 } )$ .

• A) \(\sqrt [ 3 ] { 30 }\)
• B) \(\sqrt [ 3 ] { 12 }\)
• C) \(30\)
• D)1
• E) \(\sqrt [ 3 ] { 3 }\)
• F) \(\sqrt [ 3 ] { 10 }\)
• G)12
• H)27

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Definitions:

Compounded Quarterly

The process in which interest is calculated on the principal and the accumulated interest over a quarter (three months) and is added to the principal for calculating future interest.

Accrued Interest

Interest that has accumulated over a period but has not yet been paid or officially recorded.

Nominal Interest

The stated interest rate of a loan or investment, not accounting for inflation or compounding effects.

Equivalent

Something that is equal in value, function, or meaning to another in a specified context.