\[ y'(x)=\frac {x \left (-x^6+3 x^4 y(x)^2+x^4-3 x^2 y(x)^4-2 x^2 y(x)^2+y(x)^6+y(x)^4+1\right )}{y(x)} \] ✓ Mathematica : cpu = 0.460999 (sec), leaf count = 71
DSolve[Derivative[1][y][x] == (x*(1 + x^4 - x^6 - 2*x^2*y[x]^2 + 3*x^4*y[x]^2 + y[x]^4 - 3*x^2*y[x]^4 + y[x]^6))/y[x],y[x],x]
\[\text {Solve}\left [\frac {1}{4} \left (2 \log \left (-x^2+y(x)^2+1\right )-2 x^2-\frac {1}{y(x) (y(x)+x)}+\frac {1}{x y(x)-y(x)^2}-2 \log (x-y(x))-2 \log (y(x)+x)\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.5 (sec), leaf count = 105
dsolve(diff(y(x),x) = -(-1-y(x)^4+2*y(x)^2*x^2-x^4-y(x)^6+3*y(x)^4*x^2-3*y(x)^2*x^4+x^6)*x/y(x),y(x))
\[y \left (x \right ) = -{\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{2 \textit {\_Z}} x^{2}-2 x^{3} {\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}} \ln \left (\frac {{\mathrm e}^{2 \textit {\_Z}}-2 x \,{\mathrm e}^{\textit {\_Z}}+1}{{\mathrm e}^{\textit {\_Z}}-2 x}\right )+2 \,{\mathrm e}^{2 \textit {\_Z}} c_{1}+\textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{2 \textit {\_Z}}-2 x \,{\mathrm e}^{\textit {\_Z}}+1}{{\mathrm e}^{\textit {\_Z}}-2 x}\right ) x -4 x c_{1} {\mathrm e}^{\textit {\_Z}}-2 \textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}+1\right )}+x\]