Solve the Initial Value Problem for Y as a Function $$\sqrt { x ^ { 2 } - 81 } \frac { d y } { d x } = 1 , x > 9 , y ( 18 ) = \ln ( 2 + 9 \sqrt { 3 } )$$

question 80

Multiple Choice

Solve the initial value problem for y as a function of x.
- $$\sqrt { x ^ { 2 } - 81 } \frac { d y } { d x } = 1 , x > 9 , y ( 18 ) = \ln ( 2 + 9 \sqrt { 3 } )$$

• A) \(y = \ln \left( x + \sqrt { x ^ { 2 } - 81 } \right) + \ln ( 2 + 9 \sqrt { 3 } )\)
• B) \(y = \frac { 1 } { 18 } \ln \left( \frac { x + 9 } { x - 9 } \right) + \ln 9\)
• C) \(y = \ln \left( x + \sqrt { x ^ { 2 } - 81 } \right) + \ln ( 2 + 9 \sqrt { 3 } ) - \ln ( 18 + 9 \sqrt { 3 } )\)
• D) \(y = \ln | \sec x + \tan x | + \ln ( 2 + 9 \sqrt { 3 } )\)

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Definitions:

Arachnoid Mater

A delicate membrane that encompasses the brain and spinal cord, situated between the dura mater and the pia mater, part of the meninges.

Dura Mater

The outermost, tough layer of the meninges that surround and protect the brain and spinal cord.

Outermost

Situated farthest away from the center or from a reference point.

Pia Mater

The delicate innermost layer of the meninges, the membranes surrounding the brain and spinal cord.