Solve the Initial Value Problem $$\frac { d y } { d x } = x ^ { 4 } \left( x ^ { 5 } - 5 \right) ^ { 2 } , \quad y ( 1 ) = 5$$

question 124

Multiple Choice

Solve the initial value problem.
- $$\frac { d y } { d x } = x ^ { 4 } \left( x ^ { 5 } - 5 \right) ^ { 2 } , \quad y ( 1 ) = 5$$

• A) \(y = \frac { 1 } { 15 } x ^ { 15 } - 5 + \frac { 8 } { 5 }\)
• B) \(y = \frac { 1 } { 15 } \left( x ^ { 5 } - 5 \right) ^ { 3 } + \frac { 139 } { 15 }\)
• C) \(y = \frac { 1 } { 5 } \left( x ^ { 5 } - 5 \right) ^ { 1 } + \frac { 29 } { 5 }\)
• D) \(y = \frac { 1 } { 3 } \left( x ^ { 5 } - 5 \right) ^ { 3 } + \frac { 19 } { 15 }\)

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Definitions:

Cognitive Development

The process through which a person learns to reason, solve problems, and understand concepts.

Affordances

Refers to the actional properties of objects—their nature, opportunities, and limits.

Habituation

The process of becoming accustomed to a stimulus after repeated exposure, leading to a decrease in response.

Voluntary Reaching

The deliberate extension of the arm and hand towards an object, seen as a key developmental milestone in infants.