Find the Solution of the Initial-Value Problem $\frac { d y } { d t } = 3 y + 1$

question 95

Multiple Choice

Find the solution of the initial-value problem $\frac { d y } { d t } = 3 y + 1$ , $y ( 0 ) = 2$ .

• A) \(y = \frac { 1 } { 3 } \left( 7 e ^ { t } - 1 \right)\)
• B) \(y = \left( 7 e ^ { t } - 5 \right)\)
• C) \(y = \frac { 1 } { 3 } \left( e ^ { 3 t } - 1 \right)\)
• D) \(y = \left( 3 e ^ { 3 t } - 1 \right)\)
• E) \(y = \frac { 1 } { 3 } \left( 5 e ^ { 3 t } + 1 \right)\)
• F) \(y = \left( 5 e ^ { 3 t } + 1 \right)\)
• G) \(y = \frac { 1 } { 3 } \left( 7 e ^ { 3 t } - 1 \right)\)
• H) \(y = \left( 7 e ^ { 3 t } - 1 \right)\)

---

Definitions:

Baumrind's Parenting Styles

A model that classifies parental behaviors into three main types: authoritarian, permissive, and authoritative, based on the level of responsiveness and demandingness.

Power Assertion

A disciplinary tactic employed by parents or caregivers involving the use of authority, threats, or physical force to enforce child compliance.

Authoritarian

describes a leadership or governing style characterized by strict obedience to authority at the expense of personal freedom.

Language Acquisition Device (LAD)

A hypothetical module of the human mind posited to account for children's innate predisposition for language acquisition.