2.199   ODE No. 199

\[ \sin (2 x) y'(x)+\sin (2 y(x))=0 \]

✓ Mathematica : cpu = 0.075734 (sec), leaf count = 45

DSolve[Sin[2*y[x]] + Sin[2*x]*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\frac {1}{2} \cos ^{-1}\left (-\tanh \left (\tanh ^{-1}(\cos (2 x))+2 c_1\right )\right )\right \},\left \{y(x)\to \frac {1}{2} \cos ^{-1}\left (-\tanh \left (\tanh ^{-1}(\cos (2 x))+2 c_1\right )\right )\right \}\right \}\]

✓ Maple : cpu = 0.7 (sec), leaf count = 105

dsolve(sin(2*x)*diff(y(x),x)+sin(2*y(x)) = 0,y(x))
 

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