\[ y'(x)=\frac {x}{x^4+2 x^2 y(x)^2+y(x)^4-y(x)} \] ✓ Mathematica : cpu = 0.150396 (sec), leaf count = 510
DSolve[Derivative[1][y][x] == x/(x^4 - y[x] + 2*x^2*y[x]^2 + y[x]^4),y[x],x]
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{144 c_1 x^2+\sqrt {4 \left (12 x^2-4 c_1{}^2\right ){}^3+\left (144 c_1 x^2-108+16 c_1{}^3\right ){}^2}-108+16 c_1{}^3}}{6 \sqrt [3]{2}}-\frac {12 x^2-4 c_1{}^2}{3\ 2^{2/3} \sqrt [3]{144 c_1 x^2+\sqrt {4 \left (12 x^2-4 c_1{}^2\right ){}^3+\left (144 c_1 x^2-108+16 c_1{}^3\right ){}^2}-108+16 c_1{}^3}}+\frac {c_1}{3}\right \},\left \{y(x)\to -\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{144 c_1 x^2+\sqrt {4 \left (12 x^2-4 c_1{}^2\right ){}^3+\left (144 c_1 x^2-108+16 c_1{}^3\right ){}^2}-108+16 c_1{}^3}}{12 \sqrt [3]{2}}+\frac {\left (1+i \sqrt {3}\right ) \left (12 x^2-4 c_1{}^2\right )}{6\ 2^{2/3} \sqrt [3]{144 c_1 x^2+\sqrt {4 \left (12 x^2-4 c_1{}^2\right ){}^3+\left (144 c_1 x^2-108+16 c_1{}^3\right ){}^2}-108+16 c_1{}^3}}+\frac {c_1}{3}\right \},\left \{y(x)\to -\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{144 c_1 x^2+\sqrt {4 \left (12 x^2-4 c_1{}^2\right ){}^3+\left (144 c_1 x^2-108+16 c_1{}^3\right ){}^2}-108+16 c_1{}^3}}{12 \sqrt [3]{2}}+\frac {\left (1-i \sqrt {3}\right ) \left (12 x^2-4 c_1{}^2\right )}{6\ 2^{2/3} \sqrt [3]{144 c_1 x^2+\sqrt {4 \left (12 x^2-4 c_1{}^2\right ){}^3+\left (144 c_1 x^2-108+16 c_1{}^3\right ){}^2}-108+16 c_1{}^3}}+\frac {c_1}{3}\right \}\right \}\] ✓ Maple : cpu = 0.2 (sec), leaf count = 621
dsolve(diff(y(x),x) = x/(-y(x)+x^4+2*x^2*y(x)^2+y(x)^4),y(x))
\[y \left (x \right ) = \frac {\left (-36 x^{2} c_{1}-54-c_{1}^{3}+6 \sqrt {48 x^{6}+24 x^{4} c_{1}^{2}+3 x^{2} c_{1}^{4}+108 x^{2} c_{1}+3 c_{1}^{3}+81}\right )^{\frac {1}{3}}}{6}+\frac {-12 x^{2}+c_{1}^{2}}{6 \left (-36 x^{2} c_{1}-54-c_{1}^{3}+6 \sqrt {48 x^{6}+24 x^{4} c_{1}^{2}+3 x^{2} c_{1}^{4}+108 x^{2} c_{1}+3 c_{1}^{3}+81}\right )^{\frac {1}{3}}}-\frac {c_{1}}{6}\]