\[ 3 x \left (x^2-1\right ) y'(x)-\left (x^2+1\right ) y(x)+x y(x)^2-3 x=0 \] ✓ Mathematica : cpu = 0.608678 (sec), leaf count = 2833
\[\left \{\left \{y(x)\to \frac {3 \left (x^2-1\right ) \left (c_1 \left (\frac {e^{\int _1^x\text {Root}\left [125 K[1]^8-164 K[1]^6+70 K[1]^4-20 K[1]^2+\left (1296 K[1]^{12}-5184 K[1]^{10}+7776 K[1]^8-5184 K[1]^6+1296 K[1]^4\right ) \text {$\#$1}^4+\left (-3456 K[1]^{11}+12096 K[1]^9-15552 K[1]^7+8640 K[1]^5-1728 K[1]^3\right ) \text {$\#$1}^3+\left (3240 K[1]^{10}-9504 K[1]^8+9936 K[1]^6-4320 K[1]^4+648 K[1]^2\right ) \text {$\#$1}^2+\left (-1200 K[1]^9+2736 K[1]^7-2160 K[1]^5+720 K[1]^3-96 K[1]\right ) \text {$\#$1}+5\& ,1\right ]dK[1]} \text {Root}\left [125 x^8-164 x^6+70 x^4-20 x^2+\left (1296 x^{12}-5184 x^{10}+7776 x^8-5184 x^6+1296 x^4\right ) \text {$\#$1}^4+\left (-3456 x^{11}+12096 x^9-15552 x^7+8640 x^5-1728 x^3\right ) \text {$\#$1}^3+\left (3240 x^{10}-9504 x^8+9936 x^6-4320 x^4+648 x^2\right ) \text {$\#$1}^2+\left (-1200 x^9+2736 x^7-2160 x^5+720 x^3-96 x\right ) \text {$\#$1}+5\& ,1\right ]}{\sqrt [6]{x} \sqrt [3]{1-x^2}}-\frac {e^{\int _1^x\text {Root}\left [125 K[1]^8-164 K[1]^6+70 K[1]^4-20 K[1]^2+\left (1296 K[1]^{12}-5184 K[1]^{10}+7776 K[1]^8-5184 K[1]^6+1296 K[1]^4\right ) \text {$\#$1}^4+\left (-3456 K[1]^{11}+12096 K[1]^9-15552 K[1]^7+8640 K[1]^5-1728 K[1]^3\right ) \text {$\#$1}^3+\left (3240 K[1]^{10}-9504 K[1]^8+9936 K[1]^6-4320 K[1]^4+648 K[1]^2\right ) \text {$\#$1}^2+\left (-1200 K[1]^9+2736 K[1]^7-2160 K[1]^5+720 K[1]^3-96 K[1]\right ) \text {$\#$1}+5\& ,1\right ]dK[1]}}{6 x^{7/6} \sqrt [3]{1-x^2}}+\frac {2 e^{\int _1^x\text {Root}\left [125 K[1]^8-164 K[1]^6+70 K[1]^4-20 K[1]^2+\left (1296 K[1]^{12}-5184 K[1]^{10}+7776 K[1]^8-5184 K[1]^6+1296 K[1]^4\right ) \text {$\#$1}^4+\left (-3456 K[1]^{11}+12096 K[1]^9-15552 K[1]^7+8640 K[1]^5-1728 K[1]^3\right ) \text {$\#$1}^3+\left (3240 K[1]^{10}-9504 K[1]^8+9936 K[1]^6-4320 K[1]^4+648 K[1]^2\right ) \text {$\#$1}^2+\left (-1200 K[1]^9+2736 K[1]^7-2160 K[1]^5+720 K[1]^3-96 K[1]\right ) \text {$\#$1}+5\& ,1\right ]dK[1]} x^{5/6}}{3 \left (1-x^2\right )^{4/3}}\right )+\frac {e^{\int _1^x\text {Root}\left [125 K[1]^8-164 K[1]^6+70 K[1]^4-20 K[1]^2+\left (1296 K[1]^{12}-5184 K[1]^{10}+7776 K[1]^8-5184 K[1]^6+1296 K[1]^4\right ) \text {$\#$1}^4+\left (-3456 K[1]^{11}+12096 K[1]^9-15552 K[1]^7+8640 K[1]^5-1728 K[1]^3\right ) \text {$\#$1}^3+\left (3240 K[1]^{10}-9504 K[1]^8+9936 K[1]^6-4320 K[1]^4+648 K[1]^2\right ) \text {$\#$1}^2+\left (-1200 K[1]^9+2736 K[1]^7-2160 K[1]^5+720 K[1]^3-96 K[1]\right ) \text {$\#$1}+5\& ,1\right ]dK[1]} \text {Root}\left [125 x^8-164 x^6+70 x^4-20 x^2+\left (1296 x^{12}-5184 x^{10}+7776 x^8-5184 x^6+1296 x^4\right ) \text {$\#$1}^4+\left (-3456 x^{11}+12096 x^9-15552 x^7+8640 x^5-1728 x^3\right ) \text {$\#$1}^3+\left (3240 x^{10}-9504 x^8+9936 x^6-4320 x^4+648 x^2\right ) \text {$\#$1}^2+\left (-1200 x^9+2736 x^7-2160 x^5+720 x^3-96 x\right ) \text {$\#$1}+5\& ,1\right ] \int _1^xe^{-2 \int _1^{K[2]}\text {Root}\left [125 K[1]^8-164 K[1]^6+70 K[1]^4-20 K[1]^2+\left (1296 K[1]^{12}-5184 K[1]^{10}+7776 K[1]^8-5184 K[1]^6+1296 K[1]^4\right ) \text {$\#$1}^4+\left (-3456 K[1]^{11}+12096 K[1]^9-15552 K[1]^7+8640 K[1]^5-1728 K[1]^3\right ) \text {$\#$1}^3+\left (3240 K[1]^{10}-9504 K[1]^8+9936 K[1]^6-4320 K[1]^4+648 K[1]^2\right ) \text {$\#$1}^2+\left (-1200 K[1]^9+2736 K[1]^7-2160 K[1]^5+720 K[1]^3-96 K[1]\right ) \text {$\#$1}+5\& ,1\right ]dK[1]}dK[2]}{\sqrt [6]{x} \sqrt [3]{1-x^2}}-\frac {e^{\int _1^x\text {Root}\left [125 K[1]^8-164 K[1]^6+70 K[1]^4-20 K[1]^2+\left (1296 K[1]^{12}-5184 K[1]^{10}+7776 K[1]^8-5184 K[1]^6+1296 K[1]^4\right ) \text {$\#$1}^4+\left (-3456 K[1]^{11}+12096 K[1]^9-15552 K[1]^7+8640 K[1]^5-1728 K[1]^3\right ) \text {$\#$1}^3+\left (3240 K[1]^{10}-9504 K[1]^8+9936 K[1]^6-4320 K[1]^4+648 K[1]^2\right ) \text {$\#$1}^2+\left (-1200 K[1]^9+2736 K[1]^7-2160 K[1]^5+720 K[1]^3-96 K[1]\right ) \text {$\#$1}+5\& ,1\right ]dK[1]} \int _1^xe^{-2 \int _1^{K[2]}\text {Root}\left [125 K[1]^8-164 K[1]^6+70 K[1]^4-20 K[1]^2+\left (1296 K[1]^{12}-5184 K[1]^{10}+7776 K[1]^8-5184 K[1]^6+1296 K[1]^4\right ) \text {$\#$1}^4+\left (-3456 K[1]^{11}+12096 K[1]^9-15552 K[1]^7+8640 K[1]^5-1728 K[1]^3\right ) \text {$\#$1}^3+\left (3240 K[1]^{10}-9504 K[1]^8+9936 K[1]^6-4320 K[1]^4+648 K[1]^2\right ) \text {$\#$1}^2+\left (-1200 K[1]^9+2736 K[1]^7-2160 K[1]^5+720 K[1]^3-96 K[1]\right ) \text {$\#$1}+5\& ,1\right ]dK[1]}dK[2]}{6 x^{7/6} \sqrt [3]{1-x^2}}+\frac {2 e^{\int _1^x\text {Root}\left [125 K[1]^8-164 K[1]^6+70 K[1]^4-20 K[1]^2+\left (1296 K[1]^{12}-5184 K[1]^{10}+7776 K[1]^8-5184 K[1]^6+1296 K[1]^4\right ) \text {$\#$1}^4+\left (-3456 K[1]^{11}+12096 K[1]^9-15552 K[1]^7+8640 K[1]^5-1728 K[1]^3\right ) \text {$\#$1}^3+\left (3240 K[1]^{10}-9504 K[1]^8+9936 K[1]^6-4320 K[1]^4+648 K[1]^2\right ) \text {$\#$1}^2+\left (-1200 K[1]^9+2736 K[1]^7-2160 K[1]^5+720 K[1]^3-96 K[1]\right ) \text {$\#$1}+5\& ,1\right ]dK[1]} x^{5/6} \int _1^xe^{-2 \int _1^{K[2]}\text {Root}\left [125 K[1]^8-164 K[1]^6+70 K[1]^4-20 K[1]^2+\left (1296 K[1]^{12}-5184 K[1]^{10}+7776 K[1]^8-5184 K[1]^6+1296 K[1]^4\right ) \text {$\#$1}^4+\left (-3456 K[1]^{11}+12096 K[1]^9-15552 K[1]^7+8640 K[1]^5-1728 K[1]^3\right ) \text {$\#$1}^3+\left (3240 K[1]^{10}-9504 K[1]^8+9936 K[1]^6-4320 K[1]^4+648 K[1]^2\right ) \text {$\#$1}^2+\left (-1200 K[1]^9+2736 K[1]^7-2160 K[1]^5+720 K[1]^3-96 K[1]\right ) \text {$\#$1}+5\& ,1\right ]dK[1]}dK[2]}{3 \left (1-x^2\right )^{4/3}}+\frac {e^{-\int _1^x\text {Root}\left [125 K[1]^8-164 K[1]^6+70 K[1]^4-20 K[1]^2+\left (1296 K[1]^{12}-5184 K[1]^{10}+7776 K[1]^8-5184 K[1]^6+1296 K[1]^4\right ) \text {$\#$1}^4+\left (-3456 K[1]^{11}+12096 K[1]^9-15552 K[1]^7+8640 K[1]^5-1728 K[1]^3\right ) \text {$\#$1}^3+\left (3240 K[1]^{10}-9504 K[1]^8+9936 K[1]^6-4320 K[1]^4+648 K[1]^2\right ) \text {$\#$1}^2+\left (-1200 K[1]^9+2736 K[1]^7-2160 K[1]^5+720 K[1]^3-96 K[1]\right ) \text {$\#$1}+5\& ,1\right ]dK[1]}}{\sqrt [6]{x} \sqrt [3]{1-x^2}}\right )}{\frac {e^{\int _1^x\text {Root}\left [125 K[1]^8-164 K[1]^6+70 K[1]^4-20 K[1]^2+\left (1296 K[1]^{12}-5184 K[1]^{10}+7776 K[1]^8-5184 K[1]^6+1296 K[1]^4\right ) \text {$\#$1}^4+\left (-3456 K[1]^{11}+12096 K[1]^9-15552 K[1]^7+8640 K[1]^5-1728 K[1]^3\right ) \text {$\#$1}^3+\left (3240 K[1]^{10}-9504 K[1]^8+9936 K[1]^6-4320 K[1]^4+648 K[1]^2\right ) \text {$\#$1}^2+\left (-1200 K[1]^9+2736 K[1]^7-2160 K[1]^5+720 K[1]^3-96 K[1]\right ) \text {$\#$1}+5\& ,1\right ]dK[1]} c_1}{\sqrt [6]{x} \sqrt [3]{1-x^2}}+\frac {e^{\int _1^x\text {Root}\left [125 K[1]^8-164 K[1]^6+70 K[1]^4-20 K[1]^2+\left (1296 K[1]^{12}-5184 K[1]^{10}+7776 K[1]^8-5184 K[1]^6+1296 K[1]^4\right ) \text {$\#$1}^4+\left (-3456 K[1]^{11}+12096 K[1]^9-15552 K[1]^7+8640 K[1]^5-1728 K[1]^3\right ) \text {$\#$1}^3+\left (3240 K[1]^{10}-9504 K[1]^8+9936 K[1]^6-4320 K[1]^4+648 K[1]^2\right ) \text {$\#$1}^2+\left (-1200 K[1]^9+2736 K[1]^7-2160 K[1]^5+720 K[1]^3-96 K[1]\right ) \text {$\#$1}+5\& ,1\right ]dK[1]} \int _1^xe^{-2 \int _1^{K[2]}\text {Root}\left [125 K[1]^8-164 K[1]^6+70 K[1]^4-20 K[1]^2+\left (1296 K[1]^{12}-5184 K[1]^{10}+7776 K[1]^8-5184 K[1]^6+1296 K[1]^4\right ) \text {$\#$1}^4+\left (-3456 K[1]^{11}+12096 K[1]^9-15552 K[1]^7+8640 K[1]^5-1728 K[1]^3\right ) \text {$\#$1}^3+\left (3240 K[1]^{10}-9504 K[1]^8+9936 K[1]^6-4320 K[1]^4+648 K[1]^2\right ) \text {$\#$1}^2+\left (-1200 K[1]^9+2736 K[1]^7-2160 K[1]^5+720 K[1]^3-96 K[1]\right ) \text {$\#$1}+5\& ,1\right ]dK[1]}dK[2]}{\sqrt [6]{x} \sqrt [3]{1-x^2}}}\right \}\right \}\] ✓ Maple : cpu = 0.162 (sec), leaf count = 112
\[y \relax (x ) = \frac {35 c_{1} \left (\frac {8 x^{2}}{7}-\frac {16}{35}\right ) \hypergeom \left (\left [\frac {5}{6}, \frac {7}{6}\right ], \left [\frac {4}{3}\right ], x^{2}\right )+35 \left (x^{4}-x^{2}\right ) c_{1} \hypergeom \left (\left [\frac {11}{6}, \frac {13}{6}\right ], \left [\frac {7}{3}\right ], x^{2}\right )+35 \left (-\frac {6 x^{\frac {4}{3}}}{7}+\frac {6 x^{\frac {10}{3}}}{7}\right ) \hypergeom \left (\left [\frac {3}{2}, \frac {11}{6}\right ], \left [\frac {5}{3}\right ], x^{2}\right )+24 \hypergeom \left (\left [\frac {1}{2}, \frac {5}{6}\right ], \left [\frac {2}{3}\right ], x^{2}\right ) x^{\frac {4}{3}}}{x^{\frac {1}{3}} \left (8 x^{\frac {2}{3}} \hypergeom \left (\left [\frac {5}{6}, \frac {7}{6}\right ], \left [\frac {4}{3}\right ], x^{2}\right ) c_{1}+8 \hypergeom \left (\left [\frac {1}{2}, \frac {5}{6}\right ], \left [\frac {2}{3}\right ], x^{2}\right )\right )}\]