Solve the Initial Value Problem $$\frac { d y } { d x } = x \left( 5 + x ^ { 2 } \right) ^ { 6 } , y ( 0 ) = 0$$

question 152

Multiple Choice

Solve the initial value problem.
- $$\frac { d y } { d x } = x \left( 5 + x ^ { 2 } \right) ^ { 6 } , y ( 0 ) = 0$$

• A) \(y = \frac { 1 } { 14 } \left( 5 + x ^ { 2 } \right) ^ { 7 } - \frac { 78125 } { 14 }\)
• B) \(y = \frac { 1 } { 7 } \left( 5 + x ^ { 2 } \right) ^ { 7 }\)
• C) \(y = \frac { 1 } { 14 } \left( 5 + x ^ { 2 } \right) ^ { 7 }\)
• D) \(y = \frac { 1 } { 7 } \left( 5 + x ^ { 2 } \right) ^ { 7 } - \frac { 78125 } { 7 }\)

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Definitions:

Variables

Elements, features, or factors that are likely to vary or change within the context of a study or an experiment.

Dual-route Theories

Theoretical approaches suggesting two separate pathways or mechanisms in the brain for processing information, often used in the context of reading and language comprehension.

External Theories

Concepts or explanations developed to understand phenomena outside an individual or organization, often involving the broader environment or society.

Consequences of Behavior

The outcomes or impacts that result from actions of an individual or group.