2.350   ODE No. 350

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ y'(x) \cos (y(x))-\sin (y(x))-\cos (x) \sin ^2(y(x))=0 \] Mathematica : cpu = 0.654024 (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 = 0.872 (sec), leaf count = 226

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