Solve the Initial Value Problem $$t \frac { d y } { d t } + 4 y = t ^ { 3 } ; t > 0 , y ( 2 ) = 1$$

question 76

Multiple Choice

Solve the initial value problem.
- $$t \frac { d y } { d t } + 4 y = t ^ { 3 } ; t > 0 , y ( 2 ) = 1$$

• A) \(y = \frac { t ^ { 3 } } { 7 } + \frac { 144 } { 7 } t ^ { - 4 } , t > 0\)
• B) \(y = \frac { t ^ { 3 } } { 7 } - \frac { 16 } { 7 } t ^ { - 4 } , t > 0\)
• C) \(y = \frac { t ^ { 3 } } { 7 } - 2 t ^ { - 4 } , t > 0\)
• D) \(y = \frac { t ^ { 3 } } { 7 } + \frac { 16 } { 7 } t ^ { - 4 } , t > 0\)

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Definitions:

Leadership Making

Leadership making refers to the process of developing, shaping, and evolving leadership capabilities and relationships over time, both in individuals and within organizations.

Stranger Phase

The initial stage in some interpersonal and group development processes where individuals are not yet familiar or comfortable with each other.

Leadership Making

An approach that emphasizes the development of high-quality leader-member exchanges, aiming to transform average LMX relationships into partnerships characterized by mutual respect, trust, and obligation.

Stranger Phase

The initial phase in Leader-Member Exchange (LMX) theory where the leader and the subordinate start their relationship with formal interactions based on organizational roles.