2.347   ODE No. 347

\[ (\sin (x)+1) y'(x) \sin (y(x))+\cos (x) (\cos (y(x))-1)=0 \]

✓ Mathematica : cpu = 0.558928 (sec), leaf count = 32

DSolve[Cos[x]*(-1 + Cos[y[x]]) + (1 + Sin[x])*Sin[y[x]]*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\{y(x)\to 0\},\left \{y(x)\to 2 \sin ^{-1}\left (\frac {1}{4} c_1 \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )\right )\right \}\right \}\]

✓ Maple : cpu = 0.197 (sec), leaf count = 12

dsolve(diff(y(x),x)*(1+sin(x))*sin(y(x))+cos(x)*(cos(y(x))-1) = 0,y(x))
 

\[y \left (x \right ) = \arccos \left (\sin \left (x \right ) c_{1} +c_{1} +1\right )\]