2.199   ODE No. 199

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

\[ \sin (2 x) y'(x)+\sin (2 y(x))=0 \] Mathematica : cpu = 0.232108 (sec), leaf count = 15

\[\left \{\left \{y(x)\to \cot ^{-1}\left (e^{-2 c_1} \tan (x)\right )\right \}\right \}\] Maple : cpu = 0.181 (sec), leaf count = 102

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