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) \(y = - 1 + 3 t + t ^ { 2 }\)

Apply the formulas for expected value, standard deviation, and probability in binomial and normal distributions.

Understand the importance of sample size in approximating binomial distributions with normal distributions.

Apply knowledge of probability distributions to interpret and perform calculations regarding real-life scenarios.

Understand the concept of probability in the context of random sampling and its calculation in different scenarios.

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