2.350   ODE No. 350

\[ y'(x) \cos (y(x))-\sin (y(x))-\cos (x) \sin ^2(y(x))=0 \] Mathematica : cpu = 0.578619 (sec), leaf count = 53


\[\left \{\left \{y(x)\to \csc ^{-1}\left (\frac {1}{2} \left (-\sin (x)-\cos (x)-2 c_1 e^{-x}\right )\right )\right \},\left \{y(x)\to -\csc ^{-1}\left (\frac {1}{2} \left (\sin (x)+\cos (x)+2 c_1 e^{-x}\right )\right )\right \}\right \}\] Maple : cpu = 1.043 (sec), leaf count = 226


\[y \relax (x ) = \arctan \left (-\frac {2 \,{\mathrm e}^{x}}{{\mathrm e}^{x} \left (\cos \relax (x )+\sin \relax (x )\right )+2 c_{1}}, \frac {\sqrt {16}\, \sqrt {\left (\left (\frac {\sin \relax (x ) \cos \relax (x )}{2}+\frac {1}{4}\right ) {\mathrm e}^{2 x}+{\mathrm e}^{x} \left (\cos \relax (x )+\sin \relax (x )\right ) c_{1}+c_{1}^{2}\right ) \left (\left (\frac {\sin \relax (x ) \cos \relax (x )}{2}-\frac {3}{4}\right ) {\mathrm e}^{2 x}+{\mathrm e}^{x} \left (\cos \relax (x )+\sin \relax (x )\right ) c_{1}+c_{1}^{2}\right )}}{4 c_{1}^{2}+4 \,{\mathrm e}^{x} \left (\cos \relax (x )+\sin \relax (x )\right ) c_{1}+{\mathrm e}^{2 x} \left (2 \sin \relax (x ) \cos \relax (x )+1\right )}\right )\]