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

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

---

Definitions:

Positive Reinforcement

A concept in behavior psychology where the introduction of a stimulus following a desired behavior increases the likelihood of the behavior occurring again in the future.

Negative Reinforcement

A behavioral strategy that increases the likelihood of a response by removing an unpleasant stimulus.

Modeling

The process of creating representations of complex real-world phenomena to predict outcomes or understand mechanisms, often used in science and economics.

Punishment

A penalty imposed on someone for a wrongdoing or transgression, intended as correction or deterrence.