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:

Desired Rate of Return

The minimum percentage return an investor expects to achieve on an investment, influencing the choice of investment.

Straight-Line Depreciation

An approach to distribute the cost of a tangible asset evenly over each year of its expected life.

Fixed Asset

Long-term tangible property or equipment that a firm owns and uses in its operations to generate income, not expected to be consumed or converted into cash within a year.

Cash Payback Method

A capital budgeting technique that estimates the time required to recoup the initial investment in a project, using cash inflows.