#### 2.350   ODE No. 350

$y'(x) \cos (y(x))-\sin (y(x))-\cos (x) \sin ^2(y(x))=0$ Mathematica : cpu = 0.547628 (sec), leaf count = 53

$\left \{\left \{y(x)\to \csc ^{-1}\left (\frac {1}{2} \left (-2 c_1 e^{-x}-\sin (x)-\cos (x)\right )\right )\right \},\left \{y(x)\to -\csc ^{-1}\left (\frac {1}{2} \left (2 c_1 e^{-x}+\sin (x)+\cos (x)\right )\right )\right \}\right \}$ Maple : cpu = 0.677 (sec), leaf count = 226

$\left \{ y \left ( x \right ) =\arctan \left ( -2\,{\frac {{{\rm e}^{x}}}{{{\rm e}^{x}} \left ( \cos \left ( x \right ) +\sin \left ( x \right ) \right ) +2\,{\it \_C1}}},{\frac {\sqrt {16}}{4\,{{\it \_C1}}^{2}+4\,{{\rm e}^{x}} \left ( \cos \left ( x \right ) +\sin \left ( x \right ) \right ) {\it \_C1}+ \left ( {{\rm e}^{x}} \right ) ^{2} \left ( 2\,\sin \left ( x \right ) \cos \left ( x \right ) +1 \right ) }\sqrt { \left ( \left ( {\frac {\sin \left ( x \right ) \cos \left ( x \right ) }{2}}+{\frac {1}{4}} \right ) \left ( {{\rm e}^{x}} \right ) ^{2}+{{\rm e}^{x}} \left ( \cos \left ( x \right ) +\sin \left ( x \right ) \right ) {\it \_C1}+{{\it \_C1}}^{2} \right ) \left ( \left ( {\frac {\sin \left ( x \right ) \cos \left ( x \right ) }{2}}-{\frac {3}{4}} \right ) \left ( {{\rm e}^{x}} \right ) ^{2}+{{\rm e}^{x}} \left ( \cos \left ( x \right ) +\sin \left ( x \right ) \right ) {\it \_C1}+{{\it \_C1}}^{2} \right ) }} \right ) ,y \left ( x \right ) =\arctan \left ( -2\,{\frac {{{\rm e}^{x}}}{{{\rm e}^{x}} \left ( \cos \left ( x \right ) +\sin \left ( x \right ) \right ) +2\,{\it \_C1}}},-{\frac {\sqrt {16}}{4\,{{\it \_C1}}^{2}+4\,{{\rm e}^{x}} \left ( \cos \left ( x \right ) +\sin \left ( x \right ) \right ) {\it \_C1}+ \left ( {{\rm e}^{x}} \right ) ^{2} \left ( 2\,\sin \left ( x \right ) \cos \left ( x \right ) +1 \right ) }\sqrt { \left ( \left ( {\frac {\sin \left ( x \right ) \cos \left ( x \right ) }{2}}+{\frac {1}{4}} \right ) \left ( {{\rm e}^{x}} \right ) ^{2}+{{\rm e}^{x}} \left ( \cos \left ( x \right ) +\sin \left ( x \right ) \right ) {\it \_C1}+{{\it \_C1}}^{2} \right ) \left ( \left ( {\frac {\sin \left ( x \right ) \cos \left ( x \right ) }{2}}-{\frac {3}{4}} \right ) \left ( {{\rm e}^{x}} \right ) ^{2}+{{\rm e}^{x}} \left ( \cos \left ( x \right ) +\sin \left ( x \right ) \right ) {\it \_C1}+{{\it \_C1}}^{2} \right ) }} \right ) \right \}$