The Initial Value Problem $y ^ { \prime } = \sqrt { y ^ { 2 } - 9 } , y \left( x _ { 0 } \right) = y _ { 0 }$

question 17

Multiple Choice

The initial value problem $y ^ { \prime } = \sqrt { y ^ { 2 } - 9 } , y \left( x _ { 0 } \right) = y _ { 0 }$ has a unique solution guaranteed by Theorem 1.1 if

• A) \(y _ { 0 } = 3\)
• B) \(y _ { 0 } = - 3\)
• C) \(y _ { 0 } = 5\)
• D) \(y _ { 0 } = 0\)
• E) \(y _ { 0 } = 1\)

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Definitions:

Probability

An indicator showing the probability that a specific event will take place, represented by a numerical value ranging from 0 to 1.

Experiment

An organized experiment designed to uncover new knowledge, validate a conjecture, or confirm an existing reality.

Unbiased Coins

A theoretical or actual coin for which the probability of landing heads or tails is equal, exemplifying a fair probability scenario in random experiments.

Simple Events

Events that cannot be broken down into smaller parts and have a single outcome.