2.354   ODE No. 354

\[ y'(x) (x \sin (y(x))-1)+\cos (y(x))=0 \] Mathematica : cpu = 0.170607 (sec), leaf count = 145


\[\left \{\left \{y(x)\to -\cos ^{-1}\left (\frac {c_1 x-\sqrt {-x^2+1+c_1{}^2}}{1+c_1{}^2}\right )\right \},\left \{y(x)\to \cos ^{-1}\left (\frac {c_1 x-\sqrt {-x^2+1+c_1{}^2}}{1+c_1{}^2}\right )\right \},\left \{y(x)\to -\cos ^{-1}\left (\frac {\sqrt {-x^2+1+c_1{}^2}+c_1 x}{1+c_1{}^2}\right )\right \},\left \{y(x)\to \cos ^{-1}\left (\frac {\sqrt {-x^2+1+c_1{}^2}+c_1 x}{1+c_1{}^2}\right )\right \}\right \}\] Maple : cpu = 0.073 (sec), leaf count = 108


\[y \relax (x ) = \arctan \left (\frac {-c_{1} \sqrt {-x^{2}+c_{1}^{2}+1}+x}{c_{1}^{2}+1}, \frac {c_{1} x +\sqrt {-x^{2}+c_{1}^{2}+1}}{c_{1}^{2}+1}\right )\]