3.199   ODE No. 199

\[ \boxed { \sin \left ( 2\,x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +\sin \left ( 2\,y \left ( x \right ) \right ) =0} \]

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

Mathematica: cpu = 0.185024 (sec), leaf count = 15 \[ \left \{\left \{y(x)\to \cot ^{-1}\left (e^{-2 c_1} \tan (x)\right )\right \}\right \} \]

Maple: cpu = 0.125 (sec), leaf count = 100 \[ \left \{ y \left ( x \right ) ={\frac {1}{2}\arctan \left ( 2\,{\frac {{ \it \_C1}\, \left ( 2\,\sin \left ( 2\,x \right ) +\sin \left ( 4\,x \right ) \right ) }{-{{\it \_C1}}^{2}\cos \left ( 4\,x \right ) +{{\it \_C1}}^{2}+4\,\cos \left ( 2\,x \right ) +\cos \left ( 4\,x \right ) +3}}, -{\frac {{{\it \_C1}}^{2}\cos \left ( 4\,x \right ) -{{\it \_C1}}^{2}+4 \,\cos \left ( 2\,x \right ) +\cos \left ( 4\,x \right ) +3}{-{{\it \_C1}} ^{2}\cos \left ( 4\,x \right ) +{{\it \_C1}}^{2}+4\,\cos \left ( 2\,x \right ) +\cos \left ( 4\,x \right ) +3}} \right ) } \right \} \]