\[ y'(x)^3+x y'(x)^2-y(x)=0 \] ✓ Mathematica : cpu = 53.6486 (sec), leaf count = 1496
\[\left \{\left \{y(x)\to \frac {-16 x^4+8 \left (\sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}-12\right ) x^3-4 \left (\left (-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27\right ){}^{2/3}-9 \sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}+54\right ) x^2+6 \left (72 c_1+2 \left (-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27\right ){}^{2/3}+4 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+9 \sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}\right ) x+3 \left (4 c_1 \left (2 \left (-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27\right ){}^{2/3}+9 \sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}+54\right )+9 \left (-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27\right ){}^{2/3}+12 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+2 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )} \sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}+27 \sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}+81\right )}{24 \left (-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27\right ){}^{2/3}}\right \},\left \{y(x)\to \frac {1}{2} \left (\frac {1}{48} \left (-\frac {i \left (-i+\sqrt {3}\right ) (2 x+3)^2}{\sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}}-4 x+i \left (i+\sqrt {3}\right ) \sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}+6\right ){}^2+\frac {1}{3} x \left (-\frac {i \left (-i+\sqrt {3}\right ) (2 x+3)^2}{\sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}}-4 x+i \left (i+\sqrt {3}\right ) \sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}+6\right )-2 x+2 c_1\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\frac {1}{48} \left (\frac {i \left (i+\sqrt {3}\right ) (2 x+3)^2}{\sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}}-4 x-i \left (-i+\sqrt {3}\right ) \sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}+6\right ){}^2+\frac {1}{3} x \left (\frac {i \left (i+\sqrt {3}\right ) (2 x+3)^2}{\sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}}-4 x-i \left (-i+\sqrt {3}\right ) \sqrt [3]{-8 x^3-36 x^2-54 x+108 c_1+6 \sqrt {6} \sqrt {\left (2 c_1+1\right ) \left (-4 x^3-18 x^2-27 x+27 c_1\right )}+27}+6\right )-2 x+2 c_1\right )\right \}\right \}\]
✓ Maple : cpu = 0.04 (sec), leaf count = 1251
\[ \left \{ y \left ( x \right ) =0,y \left ( x \right ) ={1 \left ( \left ( -8\,x-6 \right ) \sqrt [3]{-36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) }}+ \left ( i \left ( -36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) } \right ) ^{{\frac {2}{3}}}-4\,i{x}^{2}-12\,ix-9\,i \right ) \sqrt {3}+ \left ( -36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) } \right ) ^{{\frac {2}{3}}}+4\,{x}^{2}+12\,x+9 \right ) \left ( \left ( 4\,x-6 \right ) \sqrt [3]{-36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) }}+ \left ( i \left ( -36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) } \right ) ^{{\frac {2}{3}}}-4\,i{x}^{2}-12\,ix-9\,i \right ) \sqrt {3}+ \left ( -36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) } \right ) ^{{\frac {2}{3}}}+4\,{x}^{2}+12\,x+9 \right ) ^{2} \left ( 13824\,{x}^{3}+62208\,{x}^{2}+93312\,x-186624\,{\it \_C1}-10368\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) }-46656 \right ) ^{-1}},y \left ( x \right ) =-{1 \left ( \left ( -4\,x+6 \right ) \sqrt [3]{-36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) }}+ \left ( i \left ( -36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) } \right ) ^{{\frac {2}{3}}}-4\,i{x}^{2}-12\,ix-9\,i \right ) \sqrt {3}- \left ( -36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) } \right ) ^{{\frac {2}{3}}}-4\,{x}^{2}-12\,x-9 \right ) ^{2} \left ( \left ( 8\,x+6 \right ) \sqrt [3]{-36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) }}+ \left ( i \left ( -36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) } \right ) ^{{\frac {2}{3}}}-4\,i{x}^{2}-12\,ix-9\,i \right ) \sqrt {3}- \left ( -36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) } \right ) ^{{\frac {2}{3}}}-4\,{x}^{2}-12\,x-9 \right ) \left ( 13824\,{x}^{3}+62208\,{x}^{2}+93312\,x-186624\,{\it \_C1}-10368\,\sqrt {-6\, \left ( 1+2\,{\it \_C1} \right ) \left ( 4\,{x}^{3}+18\,{x}^{2}-27\,{\it \_C1}+27\,x \right ) }-46656 \right ) ^{-1}},y \left ( x \right ) ={\frac {1}{216} \left ( 4\,{\frac {{x}^{2}}{\sqrt [3]{-36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-48\,{x}^{3}{\it \_C1}-216\,{\it \_C1}\,{x}^{2}-24\,{x}^{3}+324\,{{\it \_C1}}^{2}-324\,{\it \_C1}\,x-108\,{x}^{2}+162\,{\it \_C1}-162\,x}}}}+12\,{\frac {x}{\sqrt [3]{-36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-48\,{x}^{3}{\it \_C1}-216\,{\it \_C1}\,{x}^{2}-24\,{x}^{3}+324\,{{\it \_C1}}^{2}-324\,{\it \_C1}\,x-108\,{x}^{2}+162\,{\it \_C1}-162\,x}}}}-2\,x+9\,{\frac {1}{\sqrt [3]{-36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-48\,{x}^{3}{\it \_C1}-216\,{\it \_C1}\,{x}^{2}-24\,{x}^{3}+324\,{{\it \_C1}}^{2}-324\,{\it \_C1}\,x-108\,{x}^{2}+162\,{\it \_C1}-162\,x}}}}+\sqrt [3]{-36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-48\,{x}^{3}{\it \_C1}-216\,{\it \_C1}\,{x}^{2}-24\,{x}^{3}+324\,{{\it \_C1}}^{2}-324\,{\it \_C1}\,x-108\,{x}^{2}+162\,{\it \_C1}-162\,x}}+3 \right ) ^{3}}+{\frac {4\,x}{9} \left ( {1 \left ( x+{\frac {3}{2}} \right ) ^{2}{\frac {1}{\sqrt [3]{-36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-48\,{x}^{3}{\it \_C1}-216\,{\it \_C1}\,{x}^{2}-24\,{x}^{3}+324\,{{\it \_C1}}^{2}-324\,{\it \_C1}\,x-108\,{x}^{2}+162\,{\it \_C1}-162\,x}}}}}-{\frac {x}{2}}+{\frac {1}{4}\sqrt [3]{-36\,{x}^{2}-54\,x+108\,{\it \_C1}-8\,{x}^{3}+27+6\,\sqrt {-48\,{x}^{3}{\it \_C1}-216\,{\it \_C1}\,{x}^{2}-24\,{x}^{3}+324\,{{\it \_C1}}^{2}-324\,{\it \_C1}\,x-108\,{x}^{2}+162\,{\it \_C1}-162\,x}}}+{\frac {3}{4}} \right ) ^{2}} \right \} \]