Find the Solution to the Differential Equation $\frac { d y } { d x } = \frac { \cos ^ { 2 } y } { x }$

question 15

Multiple Choice

Find the solution to the differential equation $\frac { d y } { d x } = \frac { \cos ^ { 2 } y } { x }$ with $y ( 1 ) = - \frac { \pi } { 4 }$ .

• A) \(y = \tan ^ { - 1 } ( \ln | x | + 1 )\)
• B) \(y = \tan ^ { - 1 } ( \ln | x | - 1 )\)
• C) \(y = \sin ^ { - 1 } \left( \ln | x | + \frac { \sqrt { 2 } } { 2 } \right)\)
• D) \(y = \cos ^ { - 1 } \left( \ln | x | + \frac { \sqrt { 2 } } { 2 } \right)\)

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