$\text { Use a power series to solve the differential equation } y ^ { t } - 3 y = 0 \text {. }$

question 37

Multiple Choice

$\text { Use a power series to solve the differential equation } y ^ { t } - 3 y = 0 \text {. }$

• A) \(y = a _ { 0 } + e ^ { 3 x }\), where \(a _ { 0 }\) is an arbitrary constant
• B) \(y = a _ { 0 } e ^ { 3 x }\), where \(a _ { 0 }\) is an arbitrary constant
• C) \(y = a _ { 0 } e ^ { x }\), where \(a _ { 0 }\) is an arbitrary constant
• D) \(y = 3 + a _ { 0 } e ^ { z }\), where \(a _ { 0 }\) is an arbitrary constant
• E) \(y = a _ { 0 } + 3 e ^ { 3 x }\), where \(a _ { 0 }\) is an arbitrary constant

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Definitions:

Thyroxin

A hormone produced by the thyroid gland that regulates metabolism, energy production, and growth and development.

Melatonin

A substance secreted by the pineal gland that controls the rhythm of sleeping and waking.

Cerebellum

A part of the hindbrain involved in muscle coordination and balance.

Pons

A part of the brain located in the brainstem, critical for relaying messages between the brain and the spinal cord and regulating sleep.