Solve the Initial Value Problem $$\frac { d y } { d x } = \frac { 1 } { x ^ { 3 } } + x , x > 0 ; y ( 1 ) = 2$$

question 259

Multiple Choice

Solve the initial value problem.
- $$\frac { d y } { d x } = \frac { 1 } { x ^ { 3 } } + x , x > 0 ; y ( 1 ) = 2$$

• A) \(y = \frac { 4 } { x ^ { 4 } } + \frac { x ^ { 2 } } { 2 } - \frac { 5 } { 2 }\)
• B) \(y = \frac { - 1 } { 2 x ^ { 2 } } + \frac { x ^ { 2 } } { 2 }\)
• C) \(y = - \frac { 1 } { 2 x ^ { 2 } } + \frac { x ^ { 2 } } { 2 } + 2\)
• D) \(y = - \frac { 1 } { 2 x ^ { 2 } } + \frac { 5 } { 2 }\)

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Definitions:

American Call Option

An option contract that allows the holder to buy an asset at a specific price before or at the expiration of the option.

Expiration Date

In finance, it typically refers to the last day on which options or futures contracts are valid.

Value Decrease

A reduction in the worth or market value of an asset or investment over time.

American Call Option

A type of call option that can be exercised at any time before its expiration date, allowing the holder to buy the underlying asset at the specified strike price.