2.969   ODE No. 969

\[ y'(x)=\frac {\csc \left (\frac {y(x)}{2 x}\right ) \sec \left (\frac {y(x)}{2 x}\right ) \sec \left (\frac {y(x)}{x}\right ) \left (-\frac {1}{2} x y(x) \sin \left (\frac {y(x)}{x}\right )-\frac {1}{2} y(x) \sin \left (\frac {y(x)}{x}\right )+x \sin \left (\frac {y(x)}{2 x}\right ) \sin \left (\frac {y(x)}{x}\right ) \cos \left (\frac {y(x)}{2 x}\right )+\frac {1}{2} x y(x) \sin \left (\frac {y(x)}{2 x}\right ) \cos \left (\frac {y(x)}{2 x}\right )+\frac {1}{2} y(x) \sin \left (\frac {y(x)}{2 x}\right ) \cos \left (\frac {y(x)}{2 x}\right )+\frac {1}{2} x y(x) \sin \left (\frac {3 y(x)}{2 x}\right ) \cos \left (\frac {y(x)}{2 x}\right )+\frac {1}{2} y(x) \sin \left (\frac {3 y(x)}{2 x}\right ) \cos \left (\frac {y(x)}{2 x}\right )\right )}{x (x+1)} \] Mathematica : cpu = 0.240143 (sec), leaf count = 19


\[\left \{\left \{y(x)\to x \sin ^{-1}\left (\frac {e^{c_1} x}{x+1}\right )\right \}\right \}\] Maple : cpu = 0.09 (sec), leaf count = 15


\[y \relax (x ) = \arcsin \left (\frac {x c_{1}}{1+x}\right ) x\]