#### 2.744   ODE No. 744

$y'(x)=\frac {x}{x^4+2 x^2 y(x)^2+y(x)^4-y(x)}$ Mathematica : cpu = 0.162603 (sec), leaf count = 510

$\left \{\left \{y(x)\to \frac {\sqrt [3]{144 c_1 x^2+\sqrt {4 \left (12 x^2-4 c_1{}^2\right ){}^3+\left (144 c_1 x^2+16 c_1{}^3-108\right ){}^2}+16 c_1{}^3-108}}{6 \sqrt [3]{2}}-\frac {12 x^2-4 c_1{}^2}{3\ 2^{2/3} \sqrt [3]{144 c_1 x^2+\sqrt {4 \left (12 x^2-4 c_1{}^2\right ){}^3+\left (144 c_1 x^2+16 c_1{}^3-108\right ){}^2}+16 c_1{}^3-108}}+\frac {c_1}{3}\right \},\left \{y(x)\to -\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{144 c_1 x^2+\sqrt {4 \left (12 x^2-4 c_1{}^2\right ){}^3+\left (144 c_1 x^2+16 c_1{}^3-108\right ){}^2}+16 c_1{}^3-108}}{12 \sqrt [3]{2}}+\frac {\left (1+i \sqrt {3}\right ) \left (12 x^2-4 c_1{}^2\right )}{6\ 2^{2/3} \sqrt [3]{144 c_1 x^2+\sqrt {4 \left (12 x^2-4 c_1{}^2\right ){}^3+\left (144 c_1 x^2+16 c_1{}^3-108\right ){}^2}+16 c_1{}^3-108}}+\frac {c_1}{3}\right \},\left \{y(x)\to -\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{144 c_1 x^2+\sqrt {4 \left (12 x^2-4 c_1{}^2\right ){}^3+\left (144 c_1 x^2+16 c_1{}^3-108\right ){}^2}+16 c_1{}^3-108}}{12 \sqrt [3]{2}}+\frac {\left (1-i \sqrt {3}\right ) \left (12 x^2-4 c_1{}^2\right )}{6\ 2^{2/3} \sqrt [3]{144 c_1 x^2+\sqrt {4 \left (12 x^2-4 c_1{}^2\right ){}^3+\left (144 c_1 x^2+16 c_1{}^3-108\right ){}^2}+16 c_1{}^3-108}}+\frac {c_1}{3}\right \}\right \}$ Maple : cpu = 0.144 (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 \}$