\[ y'(x)^3+x y'(x)^2-y(x)=0 \] ✓ Mathematica : cpu = 43.4744 (sec), leaf count = 1758
\[\left \{\left \{y(x)\to \frac {1}{2} \left (\frac {4\ 2^{2/3} x^4}{3 \left (-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54\right ){}^{2/3}}+\frac {4 \sqrt [3]{2} x^3}{3 \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}+\frac {8\ 2^{2/3} x^3}{\left (-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54\right ){}^{2/3}}+\frac {6 \sqrt [3]{2} x^2}{\sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}+\frac {18\ 2^{2/3} x^2}{\left (-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54\right ){}^{2/3}}-\frac {x^2}{3}+\frac {1}{3} 2^{2/3} \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54} x-\frac {\sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54} x}{3 \sqrt [3]{2}}+\frac {9 \sqrt [3]{2} x}{\sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}+\frac {18\ 2^{2/3} x}{\left (-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54\right ){}^{2/3}}+x+2 c_1+\frac {\left (-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54\right ){}^{2/3}}{12\ 2^{2/3}}+\frac {\sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}{2 \sqrt [3]{2}}+\frac {9}{2^{2/3} \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}+\frac {27}{2 \sqrt [3]{2} \left (-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54\right ){}^{2/3}}+\frac {9}{4}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (3 \left (\frac {1}{6} (3-2 x)-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}{12 \sqrt [3]{2}}+\frac {\left (1+i \sqrt {3}\right ) \left (-4 x^2-12 x-9\right )}{6\ 2^{2/3} \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}\right ){}^2+4 x \left (\frac {1}{6} (3-2 x)-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}{12 \sqrt [3]{2}}+\frac {\left (1+i \sqrt {3}\right ) \left (-4 x^2-12 x-9\right )}{6\ 2^{2/3} \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}\right )-2 x+2 c_1\right )\right \},\left \{y(x)\to \frac {1}{2} \left (3 \left (\frac {1}{6} (3-2 x)-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}{12 \sqrt [3]{2}}+\frac {\left (1-i \sqrt {3}\right ) \left (-4 x^2-12 x-9\right )}{6\ 2^{2/3} \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}\right ){}^2+4 x \left (\frac {1}{6} (3-2 x)-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}{12 \sqrt [3]{2}}+\frac {\left (1-i \sqrt {3}\right ) \left (-4 x^2-12 x-9\right )}{6\ 2^{2/3} \sqrt [3]{-16 x^3-72 x^2-108 x+216 c_1+\sqrt {4 \left (-4 x^2-12 x-9\right )^3+\left (-16 x^3-72 x^2-108 x+216 c_1+54\right ){}^2}+54}}\right )-2 x+2 c_1\right )\right \}\right \}\] ✓ Maple : cpu = 0.195 (sec), leaf count = 1251
\[\left \{y \left (x \right ) = 0, y \left (x \right ) = \frac {\left (4 x^{2}+12 x +\left (4 x -6\right ) \left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}\right )^{\frac {1}{3}}+\left (-4 i x^{2}-12 i x +i \left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}\right )^{\frac {2}{3}}-9 i\right ) \sqrt {3}+\left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}\right )^{\frac {2}{3}}+9\right )^{2} \left (4 x^{2}+12 x +\left (-8 x -6\right ) \left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}\right )^{\frac {1}{3}}+\left (-4 i x^{2}-12 i x +i \left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}\right )^{\frac {2}{3}}-9 i\right ) \sqrt {3}+\left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}\right )^{\frac {2}{3}}+9\right )}{13824 x^{3}+62208 x^{2}-186624 c_{1}+93312 x -10368 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}-46656}, y \left (x \right ) = -\frac {\left (-4 x^{2}-12 x +\left (-4 x +6\right ) \left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}\right )^{\frac {1}{3}}+\left (-4 i x^{2}-12 i x +i \left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}\right )^{\frac {2}{3}}-9 i\right ) \sqrt {3}-\left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}\right )^{\frac {2}{3}}-9\right )^{2} \left (-4 x^{2}-12 x +\left (8 x +6\right ) \left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}\right )^{\frac {1}{3}}+\left (-4 i x^{2}-12 i x +i \left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}\right )^{\frac {2}{3}}-9 i\right ) \sqrt {3}-\left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}\right )^{\frac {2}{3}}-9\right )}{13824 x^{3}+62208 x^{2}-186624 c_{1}+93312 x -10368 \sqrt {-6 \left (2 c_{1}+1\right ) \left (4 x^{3}+18 x^{2}+27 x -27 c_{1}\right )}-46656}, y \left (x \right ) = \frac {4 \left (-\frac {x}{2}+\frac {\left (x +\frac {3}{2}\right )^{2}}{\left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-48 c_{1} x^{3}-24 x^{3}-216 c_{1} x^{2}-108 x^{2}-324 c_{1} x +324 c_{1}^{2}-162 x +162 c_{1}}\right )^{\frac {1}{3}}}+\frac {\left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-48 c_{1} x^{3}-24 x^{3}-216 c_{1} x^{2}-108 x^{2}-324 c_{1} x +324 c_{1}^{2}-162 x +162 c_{1}}\right )^{\frac {1}{3}}}{4}+\frac {3}{4}\right )^{2} x}{9}+\frac {\left (\frac {4 x^{2}}{\left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-48 c_{1} x^{3}-24 x^{3}-216 c_{1} x^{2}-108 x^{2}-324 c_{1} x +324 c_{1}^{2}-162 x +162 c_{1}}\right )^{\frac {1}{3}}}+\frac {12 x}{\left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-48 c_{1} x^{3}-24 x^{3}-216 c_{1} x^{2}-108 x^{2}-324 c_{1} x +324 c_{1}^{2}-162 x +162 c_{1}}\right )^{\frac {1}{3}}}-2 x +\frac {9}{\left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-48 c_{1} x^{3}-24 x^{3}-216 c_{1} x^{2}-108 x^{2}-324 c_{1} x +324 c_{1}^{2}-162 x +162 c_{1}}\right )^{\frac {1}{3}}}+\left (-8 x^{3}-36 x^{2}+108 c_{1}-54 x +27+6 \sqrt {-48 c_{1} x^{3}-24 x^{3}-216 c_{1} x^{2}-108 x^{2}-324 c_{1} x +324 c_{1}^{2}-162 x +162 c_{1}}\right )^{\frac {1}{3}}+3\right )^{3}}{216}\right \}\]