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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Groupthink

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A person assigned or elected to lead or direct a group, team, or organization.

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A significant choice or determination made after considering various factors, often having long-term impacts on an individual's life or an organization's direction.

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A preconceived opinion or judgment towards people, groups, or subjects, often based on stereotypes, without factual knowledge or experience.