2.673   ODE No. 673

\[ y'(x)=\frac {\frac {1}{2} x^2 \cos (2 y(x))+\frac {x^2}{2}-\frac {1}{2} \sin (2 y(x))}{x} \] Mathematica : cpu = 0.214557 (sec), leaf count = 23

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

\[\left \{\left \{y(x)\to \arctan \left (\frac {2 x^3+3 c_1}{6 x}\right )\right \}\right \}\] Maple : cpu = 0.362 (sec), leaf count = 17

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

\[y \left (x \right ) = \arctan \left (\frac {x^{3}+6 c_{1}}{3 x}\right )\]