2.350   ODE No. 350

\[ y'(x) \cos (y(x))-\sin (y(x))-\cos (x) \sin ^2(y(x))=0 \] Mathematica : cpu = 0.414036 (sec), leaf count = 53

DSolve[-Sin[y[x]] - Cos[x]*Sin[y[x]]^2 + Cos[y[x]]*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \csc ^{-1}\left (\frac {1}{2} \left (-\sin (x)-\cos (x)-2 c_1 e^{-x}\right )\right )\right \},\left \{y(x)\to -\csc ^{-1}\left (\frac {1}{2} \left (\sin (x)+\cos (x)+2 c_1 e^{-x}\right )\right )\right \}\right \}\] Maple : cpu = 1.102 (sec), leaf count = 221

dsolve(diff(y(x),x)*cos(y(x))-cos(x)*sin(y(x))^2-sin(y(x)) = 0,y(x))
 

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