Find the Solution of the Initial-Value Problem $\frac { d y } { d t } = 2 t y ^ { 2 } + 3 y ^ { 2 }$

question 21

Multiple Choice

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

• A) \(y = - \frac { 1 } { 1 - 3 t - t ^ { 2 } }\)
• B) \(y = \frac { 1 } { 1 - 3 t + t ^ { 2 } }\)
• C) \(y = \frac { 1 } { 1 + 3 t - t ^ { 2 } }\)
• D) \(y = \frac { 1 } { 1 - 3 t - t ^ { 2 } }\)
• E) \(y = 1 + 3 t - t ^ { 2 }\)
• F) \(y = 1 - 3 y - t ^ { 2 }\)
• G) \(y = 1 - 3 t + t ^ { 2 }\)
• H) \(y = - 1 + 3 t + t ^ { 2 }\)

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Definitions:

Trade Surplus

Occurs when the value of a country's exports exceeds the value of its imports.

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The official money of the United States, commonly utilized as a standard and reserve financial instrument globally.

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refer to goods or services purchased from other countries, which are brought into a country to meet domestic demand or for further processing.

Exports

Goods or services produced in one country and sold to buyers in another, contributing to a nation's gross domestic product.