ODE No. 350

3.350 ODE No. 350

$(\frac{d}{d x} y (x)) \cos (y (x)) - \cos (x) {(\sin (y (x)))}^{2} - \sin (y (x)) = 0$

Mathematica: cpu = 0.543569 (sec), leaf count = 53 ${{y (x) \to \csc^{- 1} (\frac{1}{2} (- 2 c_{1} e^{- x} - \sin (x) - \cos (x)))}, {y (x) \to - \csc^{- 1} (\frac{1}{2} (2 c_{1} e^{- x} + \sin (x) + \cos (x)))}}$

Maple: cpu = 0.718 (sec), leaf count = 270 ${y (x) = \arctan (- 2 \frac{e^{x}}{e^{x} \cos (x) + e^{x} \sin (x) + 2_C 1}, \frac{1}{2 \cos (x) \sin (x) {(e^{x})}^{2} + 4_C 1 \sin (x) e^{x} + 4 \cos (x)_C 1 e^{x} + 4 {_C 1}^{2} + {(e^{x})}^{2}} \sqrt{(2 \cos (x) \sin (x) {(e^{x})}^{2} + 4_C 1 \sin (x) e^{x} + 4 \cos (x)_C 1 e^{x} + 4 {_C 1}^{2} + {(e^{x})}^{2}) (2 \cos (x) \sin (x) {(e^{x})}^{2} + 4_C 1 \sin (x) e^{x} + 4 \cos (x)_C 1 e^{x} - 3 {(e^{x})}^{2} + 4 {_C 1}^{2})}), y (x) = \arctan (- 2 \frac{e^{x}}{e^{x} \cos (x) + e^{x} \sin (x) + 2_C 1}, - \frac{1}{2 \cos (x) \sin (x) {(e^{x})}^{2} + 4_C 1 \sin (x) e^{x} + 4 \cos (x)_C 1 e^{x} + 4 {_C 1}^{2} + {(e^{x})}^{2}} \sqrt{(2 \cos (x) \sin (x) {(e^{x})}^{2} + 4_C 1 \sin (x) e^{x} + 4 \cos (x)_C 1 e^{x} + 4 {_C 1}^{2} + {(e^{x})}^{2}) (2 \cos (x) \sin (x) {(e^{x})}^{2} + 4_C 1 \sin (x) e^{x} + 4 \cos (x)_C 1 e^{x} - 3 {(e^{x})}^{2} + 4 {_C 1}^{2})})}$

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