\[ y'(x)=\frac {x^3 \sin (x)+x^2 y(x)^2+2 x^2 y(x) \cos (x)+\frac {x^2}{2}+x^2 \cos (x)+\frac {1}{2} x^2 \cos (2 x)+2 x y(x)-2 x y(x) \sin (x)+x-x \sin (x)-x \sin (2 x)-2 \sin (x)+2 x \cos (x)-\frac {1}{2} \cos (2 x)+\frac {3}{2}}{x^3} \] ✓ Mathematica : cpu = 0.288619 (sec), leaf count = 30
DSolve[Derivative[1][y][x] == (3/2 + x + x^2/2 + 2*x*Cos[x] + x^2*Cos[x] - Cos[2*x]/2 + (x^2*Cos[2*x])/2 - 2*Sin[x] - x*Sin[x] + x^3*Sin[x] - x*Sin[2*x] + 2*x*y[x] + 2*x^2*Cos[x]*y[x] - 2*x*Sin[x]*y[x] + x^2*y[x]^2)/x^3,y[x],x]
\[\left \{\left \{y(x)\to -\frac {-\sin (x)+x \cos (x)+1}{x}+\frac {1}{-\log (x)+c_1}\right \}\right \}\] ✓ Maple : cpu = 0.414 (sec), leaf count = 44
dsolve(diff(y(x),x) = 1/2*(2*x^2*cos(x)+2*sin(x)*x^3-2*x*sin(x)+2*x+2*y(x)^2*x^2-4*y(x)*sin(x)*x+4*y(x)*cos(x)*x^2+4*x*y(x)+3-cos(2*x)-2*sin(2*x)*x-4*sin(x)+x^2*cos(2*x)+x^2+4*cos(x)*x)/x^3,y(x))
\[y \left (x \right ) = \frac {\left (\cos \left (x \right ) x -\sin \left (x \right )+1\right ) \ln \left (x \right )-\cos \left (x \right ) c_{1} x +\sin \left (x \right ) c_{1}+x -c_{1}}{x \left (-\ln \left (x \right )+c_{1}\right )}\]