Solve the Given Differential Equation Subject to the Specified Initial $\frac { d y } { d t } = \frac { \cos t } { 9 y } ; y ( 0 ) = 3$

question 4

Multiple Choice

Solve the given differential equation subject to the specified initial condition. $\frac { d y } { d t } = \frac { \cos t } { 9 y } ; y ( 0 ) = 3$

• A) \(y ( t ) = 3 - \sqrt { \frac { 2 } { 9 } \sin t }\)
• B) \(y ( t ) = 3 + \sqrt { \frac { 2 } { 9 } \sin t }\)
• C) \(y ( t ) = \sqrt { \frac { 2 } { 9 } \sin t + 9 }\)
• D) \(y ( t ) = \sqrt { 9 - \frac { 2 } { 9 } \sin t }\)

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Definitions:

Stomach Contractions

Involuntary movements of the stomach muscles that mix and propel contents through the gastrointestinal tract.

Hypothalamus

This part of the brain, positioned under the thalamus, serves to regulate the autonomic nervous system and the actions of the pituitary, playing a significant role in the control of body temperature, the sensations of thirst and hunger, and the overall maintenance of the body’s equilibrium.

Amygdala

Involved in memory, decision-making, and emotional reactions, the amygdala is critical in how we assess and respond to environmental threats and rewards.

Medulla

The medulla is a section of the brainstem involved in autonomic functions such as breathing, heart rate, and blood pressure control.