Solve the Differential Equation with the Given Initial Condition $y ^ { \prime } = \frac { x } { y ^ { \prime } } y ( 3 ) = 5$

question 63

Multiple Choice

Solve the differential equation with the given initial condition.
- $y ^ { \prime } = \frac { x } { y ^ { \prime } } y ( 3 ) = 5$

• A) y = \(\sqrt { x ^ { 2 } + 9 }\)
• B) y = ± \(\sqrt { x ^ { 2 } + 16 }\)
• C) y = ± \(\sqrt { x ^ { 2 } + 9 }\)
• D) y = \(\sqrt { x ^ { 2 } + 16 }\)

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Definitions:

Negative Stimulus

An unfavorable event or object that causes a decrease in a specific behavior or reaction.

Positive Reinforcement

A behavioral technique that involves providing a reward to encourage the repetition of a desired behavior.

Undesirable Behavior

Actions or conduct that are considered unacceptable or inappropriate within a specific context, often leading to negative consequences.

Extinction

In a behavioral context, extinction is the process of reducing or eliminating a learned response, typically by no longer providing the reinforcement that maintained the behavior.