\[ y'(x)^3+y'(x)-y(x)=0 \] ✓ Mathematica : cpu = 237.102 (sec), leaf count = 3323
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {\left (243 \text {$\#$1}^2-27 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-24 \sqrt [3]{2} \sqrt [6]{3} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-24 \sqrt [3]{2} \sqrt [6]{3} \tan ^{-1}\left (\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+\frac {1}{\sqrt {3}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+8 \sqrt [3]{2} 3^{2/3} \log \left (6-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+8 \sqrt [3]{2} 3^{2/3} \log \left (2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-4 \sqrt [3]{2} 3^{2/3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-4 \sqrt [3]{2} 3^{2/3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+54\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{4/3}}{864 \sqrt [3]{3} \left (-27 \text {$\#$1}^2+3 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-2\right )}+\frac {\sqrt {9 \text {$\#$1}^2+\frac {4}{3}} \left (2\ 2^{2/3} 3^{5/6} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right )+2\ 2^{2/3} 3^{5/6} \tan ^{-1}\left (\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+\frac {1}{\sqrt {3}}\right )+2\ 2^{2/3} \sqrt [3]{3} \log \left (6-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right )+2\ 2^{2/3} \sqrt [3]{3} \log \left (2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )-2^{2/3} \sqrt [3]{3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )-2^{2/3} \sqrt [3]{3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )+3 \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )}{36 \sqrt [3]{2} \left (-27 \text {$\#$1}^2+3 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-4\right )}-\frac {\left (9 \sqrt {3} \text {$\#$1}+\sqrt {27 \text {$\#$1}^2+4}\right ) \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}}{32\ 3^{5/6}}-\frac {\log (\text {$\#$1})}{3\ 6^{2/3}}\& \right ]\left [c_1-\frac {x}{6^{2/3}}\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {i \left (-\frac {\sqrt [3]{3} \left (-i+\sqrt {3}\right ) \left (243 \text {$\#$1}^2-27 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-24 \sqrt [3]{2} \sqrt [6]{3} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-24 \sqrt [3]{2} \sqrt [6]{3} \tan ^{-1}\left (\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+\frac {1}{\sqrt {3}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+8 \sqrt [3]{2} 3^{2/3} \log \left (6-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+8 \sqrt [3]{2} 3^{2/3} \log \left (2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-4 \sqrt [3]{2} 3^{2/3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-4 \sqrt [3]{2} 3^{2/3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+54\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{4/3}}{-27 \text {$\#$1}^2+3 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-2}+\frac {4\ 6^{2/3} \left (3+i \sqrt {3}\right ) \sqrt {27 \text {$\#$1}^2+4} \left (2\ 2^{2/3} 3^{5/6} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right )+2\ 2^{2/3} 3^{5/6} \tan ^{-1}\left (\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+\frac {1}{\sqrt {3}}\right )+2\ 2^{2/3} \sqrt [3]{3} \log \left (6-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right )+2\ 2^{2/3} \sqrt [3]{3} \log \left (2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )-2^{2/3} \sqrt [3]{3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )-2^{2/3} \sqrt [3]{3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )+3 \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )}{-27 \text {$\#$1}^2+3 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-4}+9 \sqrt [3]{3} \left (3-i \sqrt {3}\right ) \left (9 \sqrt {3} \text {$\#$1}+\sqrt {27 \text {$\#$1}^2+4}\right ) \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+288 i \sqrt [3]{2} \log (\text {$\#$1})\right )}{3456\ 3^{5/6}}\& \right ]\left [\frac {x}{2\ 2^{2/3} 3^{5/6}}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {i \left (-\frac {\sqrt [3]{3} \left (i+\sqrt {3}\right ) \left (243 \text {$\#$1}^2-27 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-24 \sqrt [3]{2} \sqrt [6]{3} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-24 \sqrt [3]{2} \sqrt [6]{3} \tan ^{-1}\left (\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+\frac {1}{\sqrt {3}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+8 \sqrt [3]{2} 3^{2/3} \log \left (6-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+8 \sqrt [3]{2} 3^{2/3} \log \left (2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-4 \sqrt [3]{2} 3^{2/3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-4 \sqrt [3]{2} 3^{2/3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+54\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{4/3}}{-27 \text {$\#$1}^2+3 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-2}+\frac {4\ 6^{2/3} \left (3-i \sqrt {3}\right ) \sqrt {27 \text {$\#$1}^2+4} \left (2\ 2^{2/3} 3^{5/6} \tan ^{-1}\left (\frac {1}{\sqrt {3}}-\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right )+2\ 2^{2/3} 3^{5/6} \tan ^{-1}\left (\left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+\frac {1}{\sqrt {3}}\right )+2\ 2^{2/3} \sqrt [3]{3} \log \left (6-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}\right )+2\ 2^{2/3} \sqrt [3]{3} \log \left (2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )-2^{2/3} \sqrt [3]{3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}-2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )-2^{2/3} \sqrt [3]{3} \log \left (\sqrt [3]{2} 3^{2/3} \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}+2^{2/3} 3^{5/6} \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}+6\right )+3 \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )^{2/3}\right ) \left (\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}\right )}{-27 \text {$\#$1}^2+3 \sqrt {81 \text {$\#$1}^2+12} \text {$\#$1}-4}+9 \sqrt [3]{3} \left (3+i \sqrt {3}\right ) \left (9 \sqrt {3} \text {$\#$1}+\sqrt {27 \text {$\#$1}^2+4}\right ) \sqrt [3]{\sqrt {81 \text {$\#$1}^2+12}-9 \text {$\#$1}}-288 i \sqrt [3]{2} \log (\text {$\#$1})\right )}{3456\ 3^{5/6}}\& \right ]\left [\frac {x}{2\ 2^{2/3} 3^{5/6}}+c_1\right ]\right \}\right \}\] ✓ Maple : cpu = 0.168 (sec), leaf count = 245
\[ \left \{ x-\int ^{y \left ( x \right ) }\!6\,{\frac {\sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}}{ \left ( 108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12} \right ) ^{2/3}-12}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-12\,{\frac {\sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}}{ \left ( i\sqrt {3}-1 \right ) \left ( -\sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}+\sqrt {3}+3\,i \right ) \left ( \sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}+\sqrt {3}+3\,i \right ) }}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-12\,{\frac {\sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}}{ \left ( i\sqrt {3}+1 \right ) \left ( \sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}+\sqrt {3}-3\,i \right ) \left ( \sqrt [3]{108\,{\it \_a}+12\,\sqrt {81\,{{\it \_a}}^{2}+12}}+3\,i-\sqrt {3} \right ) }}{d{\it \_a}}-{\it \_C1}=0 \right \} \]