\[ y'(x)=\frac {x}{x^4+2 x^2 y(x)^2+y(x)^4-y(x)} \] ✓ Mathematica : cpu = 0.0559614 (sec), leaf count = 534
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{144 c_1 x^2+2 \sqrt {\left (12 x^2-4 c_1^2\right ){}^3+4 \left (36 c_1 x^2+4 c_1^3-27\right ){}^2}+16 c_1^3-108}}{6 \sqrt [3]{2}}+\frac {2^{2/3} \left (c_1^2-3 x^2\right )}{3 \sqrt [3]{36 c_1 x^2+3 \sqrt {3} \sqrt {32 c_1^2 x^4+8 c_1 \left (2 c_1^3-9\right ) x^2-8 c_1^3+16 x^6+27}+4 c_1^3-27}}+\frac {c_1}{3}\right \},\left \{y(x)\to \frac {\left (-1+i \sqrt {3}\right ) \sqrt [3]{144 c_1 x^2+2 \sqrt {\left (12 x^2-4 c_1^2\right ){}^3+4 \left (36 c_1 x^2+4 c_1^3-27\right ){}^2}+16 c_1^3-108}}{12 \sqrt [3]{2}}+\frac {\left (1+i \sqrt {3}\right ) \left (3 x^2-c_1^2\right )}{3 \sqrt [3]{72 c_1 x^2+6 \sqrt {3} \sqrt {32 c_1^2 x^4+8 c_1 \left (2 c_1^3-9\right ) x^2-8 c_1^3+16 x^6+27}+8 c_1^3-54}}+\frac {c_1}{3}\right \},\left \{y(x)\to -\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{144 c_1 x^2+2 \sqrt {\left (12 x^2-4 c_1^2\right ){}^3+4 \left (36 c_1 x^2+4 c_1^3-27\right ){}^2}+16 c_1^3-108}}{12 \sqrt [3]{2}}+\frac {\left (1-i \sqrt {3}\right ) \left (3 x^2-c_1^2\right )}{3 \sqrt [3]{72 c_1 x^2+6 \sqrt {3} \sqrt {32 c_1^2 x^4+8 c_1 \left (2 c_1^3-9\right ) x^2-8 c_1^3+16 x^6+27}+8 c_1^3-54}}+\frac {c_1}{3}\right \}\right \}\]
✓ Maple : cpu = 0.216 (sec), leaf count = 621
\[ \left \{ y \left ( x \right ) =-{\frac {1}{12} \left ( 2\,{\it \_C1}\,\sqrt [3]{-36\,{\it \_C1}\,{x}^{2}-54-{{\it \_C1}}^{3}+6\,\sqrt {48\,{x}^{6}+24\,{x}^{4}{{\it \_C1}}^{2}+ \left ( 3\,{{\it \_C1}}^{4}+108\,{\it \_C1} \right ) {x}^{2}+3\,{{\it \_C1}}^{3}+81}}+ \left ( i \left ( -36\,{\it \_C1}\,{x}^{2}-54-{{\it \_C1}}^{3}+6\,\sqrt {48\,{x}^{6}+24\,{x}^{4}{{\it \_C1}}^{2}+ \left ( 3\,{{\it \_C1}}^{4}+108\,{\it \_C1} \right ) {x}^{2}+3\,{{\it \_C1}}^{3}+81} \right ) ^{{\frac {2}{3}}}+12\,i{x}^{2}-i{{\it \_C1}}^{2} \right ) \sqrt {3}+ \left ( -36\,{\it \_C1}\,{x}^{2}-54-{{\it \_C1}}^{3}+6\,\sqrt {48\,{x}^{6}+24\,{x}^{4}{{\it \_C1}}^{2}+ \left ( 3\,{{\it \_C1}}^{4}+108\,{\it \_C1} \right ) {x}^{2}+3\,{{\it \_C1}}^{3}+81} \right ) ^{{\frac {2}{3}}}-12\,{x}^{2}+{{\it \_C1}}^{2} \right ) {\frac {1}{\sqrt [3]{-36\,{\it \_C1}\,{x}^{2}-54-{{\it \_C1}}^{3}+6\,\sqrt {48\,{x}^{6}+24\,{x}^{4}{{\it \_C1}}^{2}+ \left ( 3\,{{\it \_C1}}^{4}+108\,{\it \_C1} \right ) {x}^{2}+3\,{{\it \_C1}}^{3}+81}}}}},y \left ( x \right ) ={\frac {1}{12} \left ( -2\,{\it \_C1}\,\sqrt [3]{-36\,{\it \_C1}\,{x}^{2}-54-{{\it \_C1}}^{3}+6\,\sqrt {48\,{x}^{6}+24\,{x}^{4}{{\it \_C1}}^{2}+ \left ( 3\,{{\it \_C1}}^{4}+108\,{\it \_C1} \right ) {x}^{2}+3\,{{\it \_C1}}^{3}+81}}+ \left ( i \left ( -36\,{\it \_C1}\,{x}^{2}-54-{{\it \_C1}}^{3}+6\,\sqrt {48\,{x}^{6}+24\,{x}^{4}{{\it \_C1}}^{2}+ \left ( 3\,{{\it \_C1}}^{4}+108\,{\it \_C1} \right ) {x}^{2}+3\,{{\it \_C1}}^{3}+81} \right ) ^{{\frac {2}{3}}}+12\,i{x}^{2}-i{{\it \_C1}}^{2} \right ) \sqrt {3}- \left ( -36\,{\it \_C1}\,{x}^{2}-54-{{\it \_C1}}^{3}+6\,\sqrt {48\,{x}^{6}+24\,{x}^{4}{{\it \_C1}}^{2}+ \left ( 3\,{{\it \_C1}}^{4}+108\,{\it \_C1} \right ) {x}^{2}+3\,{{\it \_C1}}^{3}+81} \right ) ^{{\frac {2}{3}}}+12\,{x}^{2}-{{\it \_C1}}^{2} \right ) {\frac {1}{\sqrt [3]{-36\,{\it \_C1}\,{x}^{2}-54-{{\it \_C1}}^{3}+6\,\sqrt {48\,{x}^{6}+24\,{x}^{4}{{\it \_C1}}^{2}+ \left ( 3\,{{\it \_C1}}^{4}+108\,{\it \_C1} \right ) {x}^{2}+3\,{{\it \_C1}}^{3}+81}}}}},y \left ( x \right ) ={\frac {1}{6}\sqrt [3]{-36\,{\it \_C1}\,{x}^{2}-54-{{\it \_C1}}^{3}+6\,\sqrt {3\,{x}^{2}{{\it \_C1}}^{4}+24\,{x}^{4}{{\it \_C1}}^{2}+48\,{x}^{6}+3\,{{\it \_C1}}^{3}+108\,{\it \_C1}\,{x}^{2}+81}}}+{\frac {{{\it \_C1}}^{2}-12\,{x}^{2}}{6}{\frac {1}{\sqrt [3]{-36\,{\it \_C1}\,{x}^{2}-54-{{\it \_C1}}^{3}+6\,\sqrt {3\,{x}^{2}{{\it \_C1}}^{4}+24\,{x}^{4}{{\it \_C1}}^{2}+48\,{x}^{6}+3\,{{\it \_C1}}^{3}+108\,{\it \_C1}\,{x}^{2}+81}}}}}-{\frac {{\it \_C1}}{6}} \right \} \]