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 = 0.562796 (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 = 1.076 (sec), leaf count = 270

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