\[ -a x y'(x)+x^3+y'(x)^3=0 \] ✓ Mathematica : cpu = 2716.63 (sec), leaf count = 389
\[\left \{\left \{y(x)\to \int _1^x \left (\frac {\sqrt [3]{\frac {2}{3}} a K[1]}{\sqrt [3]{\sqrt {3} \sqrt {27 K[1]^6-4 a^3 K[1]^3}-9 K[1]^3}}+\frac {\sqrt [3]{\sqrt {3} \sqrt {27 K[1]^6-4 a^3 K[1]^3}-9 K[1]^3}}{\sqrt [3]{2} 3^{2/3}}\right ) \, dK[1]+c_1\right \},\left \{y(x)\to c_1+\int _1^x \left (-\frac {\left (1+i \sqrt {3}\right ) a K[2]}{2^{2/3} \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {27 K[2]^6-4 a^3 K[2]^3}-9 K[2]^3}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {3} \sqrt {27 K[2]^6-4 a^3 K[2]^3}-9 K[2]^3}}{2 \sqrt [3]{2} 3^{2/3}}\right ) \, dK[2]\right \},\left \{y(x)\to c_1+\int _1^x \left (-\frac {\left (1-i \sqrt {3}\right ) a K[3]}{2^{2/3} \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {27 K[3]^6-4 a^3 K[3]^3}-9 K[3]^3}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {3} \sqrt {27 K[3]^6-4 a^3 K[3]^3}-9 K[3]^3}}{2 \sqrt [3]{2} 3^{2/3}}\right ) \, dK[3]\right \}\right \}\]
✓ Maple : cpu = 0.055 (sec), leaf count = 300
\[ \left \{ y \left ( x \right ) =\int \!{{\frac {i}{12}} \left ( i \left ( -108\,{x}^{3}+12\,\sqrt {-3\,{x}^{3} \left ( 4\,{a}^{3}-27\,{x}^{3} \right ) } \right ) ^{{\frac {2}{3}}}+12\,iax- \left ( -108\,{x}^{3}+12\,\sqrt {-3\,{x}^{3} \left ( 4\,{a}^{3}-27\,{x}^{3} \right ) } \right ) ^{{\frac {2}{3}}}\sqrt {3}+12\,\sqrt {3}ax \right ) {\frac {1}{\sqrt [3]{-108\,{x}^{3}+12\,\sqrt {-3\,{x}^{3} \left ( 4\,{a}^{3}-27\,{x}^{3} \right ) }}}}}\,{\rm d}x+{\it \_C1},y \left ( x \right ) =\int \!{{\frac {i}{12}} \left ( \left ( -108\,{x}^{3}+12\,\sqrt {-3\,{x}^{3} \left ( 4\,{a}^{3}-27\,{x}^{3} \right ) } \right ) ^{{\frac {2}{3}}}\sqrt {3}-12\,\sqrt {3}ax+i \left ( -108\,{x}^{3}+12\,\sqrt {-3\,{x}^{3} \left ( 4\,{a}^{3}-27\,{x}^{3} \right ) } \right ) ^{{\frac {2}{3}}}+12\,iax \right ) {\frac {1}{\sqrt [3]{-108\,{x}^{3}+12\,\sqrt {-3\,{x}^{3} \left ( 4\,{a}^{3}-27\,{x}^{3} \right ) }}}}}\,{\rm d}x+{\it \_C1},y \left ( x \right ) =\int \!{\frac {1}{6} \left ( \left ( -108\,{x}^{3}+12\,\sqrt {-3\,{x}^{3} \left ( 4\,{a}^{3}-27\,{x}^{3} \right ) } \right ) ^{{\frac {2}{3}}}+12\,ax \right ) {\frac {1}{\sqrt [3]{-108\,{x}^{3}+12\,\sqrt {-3\,{x}^{3} \left ( 4\,{a}^{3}-27\,{x}^{3} \right ) }}}}}\,{\rm d}x+{\it \_C1} \right \} \]