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:

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