\[ y'(x)^3-(y(x)-a)^2 (y(x)-b)^2=0 \] ✓ Mathematica : cpu = 0.59083 (sec), leaf count = 236
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \left (\frac {\text {$\#$1}-b}{a-b}\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{(b-\text {$\#$1})^{2/3}}\& \right ][x+c_1]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \left (\frac {\text {$\#$1}-b}{a-b}\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{(b-\text {$\#$1})^{2/3}}\& \right ]\left [-\sqrt [3]{-1} x+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \left (\frac {\text {$\#$1}-b}{a-b}\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{(b-\text {$\#$1})^{2/3}}\& \right ]\left [(-1)^{2/3} x+c_1\right ]\right \}\right \}\] ✓ Maple : cpu = 0.462 (sec), leaf count = 126
\[\left \{-c_{1}+x -\left (\int _{}^{y \left (x \right )}\frac {1}{\left (\left (\textit {\_a} -a \right )^{2} \left (\textit {\_a} -b \right )^{2}\right )^{\frac {1}{3}}}d \textit {\_a} \right ) = 0, -c_{1}+x -\left (\int _{}^{y \left (x \right )}-\frac {2}{\left (1+i \sqrt {3}\right ) \left (\left (-\textit {\_a} +a \right )^{2} \left (-\textit {\_a} +b \right )^{2}\right )^{\frac {1}{3}}}d \textit {\_a} \right ) = 0, -c_{1}+x -\left (\int _{}^{y \left (x \right )}\frac {2}{\left (i \sqrt {3}-1\right ) \left (\left (-\textit {\_a} +a \right )^{2} \left (-\textit {\_a} +b \right )^{2}\right )^{\frac {1}{3}}}d \textit {\_a} \right ) = 0, y \left (x \right ) = a, y \left (x \right ) = b\right \}\]