2.904   ODE No. 904

\[ y'(x)=\frac {\sin \left (\frac {y(x)}{x}\right ) \csc \left (\frac {y(x)}{2 x}\right ) \sec \left (\frac {y(x)}{2 x}\right ) \left (2 x^3 \sin \left (\frac {y(x)}{2 x}\right ) \cos \left (\frac {y(x)}{2 x}\right )+y(x)\right )}{2 x} \]

✓ Mathematica : cpu = 0.062422 (sec), leaf count = 46

DSolve[Derivative[1][y][x] == (Csc[y[x]/(2*x)]*Sec[y[x]/(2*x)]*Sin[y[x]/x]*(2*x^3*Cos[y[x]/(2*x)]*Sin[y[x]/(2*x)] + y[x]))/(2*x),y[x],x]
 

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

✓ Maple : cpu = 0.161 (sec), leaf count = 61

dsolve(diff(y(x),x) = 1/2*sin(y(x)/x)*(y(x)+2*x^3*cos(1/2*y(x)/x)*sin(1/2*y(x)/x))/sin(1/2*y(x)/x)/x/cos(1/2*y(x)/x),y(x))
 

\[y \left (x \right ) = \arctan \left (\frac {2 \,{\mathrm e}^{-\frac {x^{2}}{2}} c_{1}}{{\mathrm e}^{-x^{2}}+c_{1}^{2}}, \frac {\frac {{\mathrm e}^{-x^{2}}}{c_{1}^{2}}-1}{\frac {{\mathrm e}^{-x^{2}}}{c_{1}^{2}}+1}\right ) x\]