Solve the Initial Value Problem for Y as a Function $$\left( x ^ { 2 } + 81 \right) ^ { 2 } \frac { d y } { d x } = \sqrt { x ^ { 2 } + 81 } , y ( 0 ) = 9$$

question 423

Multiple Choice

Solve the initial value problem for y as a function of x.
- $$\left( x ^ { 2 } + 81 \right) ^ { 2 } \frac { d y } { d x } = \sqrt { x ^ { 2 } + 81 } , y ( 0 ) = 9$$

• A) \(y = \frac { x } { 9 } + 9\)
• B) \(y = \frac { x } { 81 } + 9\)
• C) \(y = \frac { x } { 81 \sqrt { x ^ { 2 } + 81 } } + 9\)
• D) \(y = \frac { x } { 81 \sqrt { x ^ { 2 } + 81 } }\)

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Definitions:

Vertical Integration

A business strategy where a company expands its operations into different stages of production within the same industry, often to increase control over the supply chain.

Upstream Price Discrimination

The practice of varying prices for goods or services at an earlier stage in the supply chain based on different buyers' willingness to pay.

Arbitrage

The practice of buying and selling the same asset in different markets to profit from price differences.

Vertical Integration

A company's expansion into different stages of production or distribution within the same industry, controlling more of its supply chain.