3.350   ODE No. 350

\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) \cos \left ( y \left ( x \right ) \right ) -\cos \left ( x \right ) \left ( \sin \left ( y \left ( x \right ) \right ) \right ) ^{2}-\sin \left ( y \left ( x \right ) \right ) =0} \]

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

Mathematica: cpu = 0.543569 (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 = 0.718 (sec), leaf count = 270 \[ \left \{ y \left ( x \right ) =\arctan \left ( -2\,{\frac {{{\rm e}^{x}} }{{{\rm e}^{x}}\cos \left ( x \right ) +{{\rm e}^{x}}\sin \left ( x \right ) +2\,{\it \_C1}}},{\frac {1}{2\,\cos \left ( x \right ) \sin \left ( x \right ) \left ( {{\rm e}^{x}} \right ) ^{2}+4\,{\it \_C1}\, \sin \left ( x \right ) {{\rm e}^{x}}+4\,\cos \left ( x \right ) {\it \_C1 }\,{{\rm e}^{x}}+4\,{{\it \_C1}}^{2}+ \left ( {{\rm e}^{x}} \right ) ^{2 }}\sqrt { \left ( 2\,\cos \left ( x \right ) \sin \left ( x \right ) \left ( {{\rm e}^{x}} \right ) ^{2}+4\,{\it \_C1}\,\sin \left ( x \right ) {{\rm e}^{x}}+4\,\cos \left ( x \right ) {\it \_C1}\,{{\rm e}^{ x}}+4\,{{\it \_C1}}^{2}+ \left ( {{\rm e}^{x}} \right ) ^{2} \right ) \left ( 2\,\cos \left ( x \right ) \sin \left ( x \right ) \left ( { {\rm e}^{x}} \right ) ^{2}+4\,{\it \_C1}\,\sin \left ( x \right ) { {\rm e}^{x}}+4\,\cos \left ( x \right ) {\it \_C1}\,{{\rm e}^{x}}-3\, \left ( {{\rm e}^{x}} \right ) ^{2}+4\,{{\it \_C1}}^{2} \right ) }} \right ) ,y \left ( x \right ) =\arctan \left ( -2\,{\frac {{{\rm e}^{x}} }{{{\rm e}^{x}}\cos \left ( x \right ) +{{\rm e}^{x}}\sin \left ( x \right ) +2\,{\it \_C1}}},-{\frac {1}{2\,\cos \left ( x \right ) \sin \left ( x \right ) \left ( {{\rm e}^{x}} \right ) ^{2}+4\,{\it \_C1}\, \sin \left ( x \right ) {{\rm e}^{x}}+4\,\cos \left ( x \right ) {\it \_C1 }\,{{\rm e}^{x}}+4\,{{\it \_C1}}^{2}+ \left ( {{\rm e}^{x}} \right ) ^{2 }}\sqrt { \left ( 2\,\cos \left ( x \right ) \sin \left ( x \right ) \left ( {{\rm e}^{x}} \right ) ^{2}+4\,{\it \_C1}\,\sin \left ( x \right ) {{\rm e}^{x}}+4\,\cos \left ( x \right ) {\it \_C1}\,{{\rm e}^{ x}}+4\,{{\it \_C1}}^{2}+ \left ( {{\rm e}^{x}} \right ) ^{2} \right ) \left ( 2\,\cos \left ( x \right ) \sin \left ( x \right ) \left ( { {\rm e}^{x}} \right ) ^{2}+4\,{\it \_C1}\,\sin \left ( x \right ) { {\rm e}^{x}}+4\,\cos \left ( x \right ) {\it \_C1}\,{{\rm e}^{x}}-3\, \left ( {{\rm e}^{x}} \right ) ^{2}+4\,{{\it \_C1}}^{2} \right ) }} \right ) \right \} \]