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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The Answer of 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) $y = \cos ^ { - 1 } \left( \ln | x | + \frac { \sqrt { 2 } } { 2 } \right)$

Find the Solution to the Differential Equation dydx=cos⁡2yx\frac { d y } { d x } = \frac { \cos ^ { 2 } y } { x }dxdy​=xcos2y​

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