\[ y'(x)=\frac {-\frac {5 x^3}{2}+\frac {15}{4} x^3 \cos (x)-\frac {3}{2} x^3 \cos (2 x)+\frac {1}{4} x^3 \cos (3 x)+\frac {9}{2} x^2 y(x)-6 x^2 y(x) \cos (x)+\frac {3}{2} x^2 y(x) \cos (2 x)+\frac {3 x^2}{2}+x^2 \sin (x)-2 x^2 \cos (x)+\frac {1}{2} x^2 \cos (2 x)-3 x y(x)^2-2 x y(x)+y(x)^3+y(x)^2+3 x y(x)^2 \cos (x)+2 x y(x) \cos (x)+x-x \cos (x)+1}{x} \] ✓ Mathematica : cpu = 0.46152 (sec), leaf count = 108
DSolve[Derivative[1][y][x] == (1 + x + (3*x^2)/2 - (5*x^3)/2 - x*Cos[x] - 2*x^2*Cos[x] + (15*x^3*Cos[x])/4 + (x^2*Cos[2*x])/2 - (3*x^3*Cos[2*x])/2 + (x^3*Cos[3*x])/4 + x^2*Sin[x] - 2*x*y[x] + (9*x^2*y[x])/2 + 2*x*Cos[x]*y[x] - 6*x^2*Cos[x]*y[x] + (3*x^2*Cos[2*x]*y[x])/2 + y[x]^2 - 3*x*y[x]^2 + 3*x*Cos[x]*y[x]^2 + y[x]^3)/x,y[x],x]
\[\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {3 y(x)}{x}+\frac {-3 x+3 x \cos (x)+1}{x}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^3}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 29^{2/3} \left (\frac {1}{x^3}\right )^{2/3} x^2 \log (x)+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.214 (sec), leaf count = 39
dsolve(diff(y(x),x) = 1/4*(-4*cos(x)*x+4*x^2*sin(x)+4*x+4+4*y(x)^2+8*y(x)*cos(x)*x-8*x*y(x)+2*x^2*cos(2*x)+6*x^2-8*x^2*cos(x)+4*y(x)^3+12*y(x)^2*cos(x)*x-12*x*y(x)^2+6*y(x)*x^2*cos(2*x)+18*x^2*y(x)-24*y(x)*cos(x)*x^2+x^3*cos(3*x)+15*x^3*cos(x)-6*x^3*cos(2*x)-10*x^3)/x,y(x))
\[y \left (x \right ) = -\cos \left (x \right ) x +x -\frac {1}{3}+\frac {29 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+\ln \left (x \right )+3 c_{1}\right )}{9}\]