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

question 59

Multiple Choice

Find the solution of the initial-value problem $\frac { d y } { d t } = \frac { 2 t } { y ^ { 2 } + t ^ { 2 } y ^ { 2 } }$ , $y ( 0 ) = 3$ .

• A) \(y = 3 \ln \left( 1 + t ^ { 2 } \right) + 3 C\)
• B) \(y = \sqrt [ 3 ] { 3 \ln \left( 1 + t ^ { 2 } \right) + 3 C }\)
• C) \(y = 3 \ln \left( 1 + t ^ { 2 } \right) + 9\)
• D) \(y = \sqrt [ 3 ] { 3 \ln \left( 1 + t ^ { 2 } \right) + 9 }\)
• E) \(y = 3 \ln \left( 1 + t ^ { 2 } \right) + 27\)
• F) \(y = \sqrt [ 3 ] { 3 \ln \left( 1 + t ^ { 2 } \right) + 27 }\)
• G) \(y = 3 \ln \left( 1 + t ^ { 2 } \right)\)
• H) \(y = \sqrt [ 3 ] { 3 \ln \left( 1 + t ^ { 2 } \right) }\)

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Definitions:

Coffee

A brewed drink prepared from roasted coffee beans, the seeds of berries from certain Coffea species.

Profit

The financial gain realized when the revenue from business activities exceeds the expenses, costs, and taxes associated with sustaining the activity.

Gram

A unit of weight that is one thousandth part of a kilogram, measured in the metric system.

Ounce

A unit of weight commonly used in the United States and the United Kingdom, equal to one-sixteenth of a pound or approximately 28.35 grams.