\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{3}- \left ( y \left ( x \right ) -a \right ) ^{2} \left ( y \left ( x \right ) -b \right ) ^{2}=0} \]
Mathematica: cpu = 0.801102 (sec), leaf count = 236 \[ \left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \left (\frac {\text {$\#$1}-b}{a-b}\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{(b-\text {$\#$1})^{2/3}}\& \right ]\left [c_1+x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \left (\frac {\text {$\#$1}-b}{a-b}\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{(b-\text {$\#$1})^{2/3}}\& \right ]\left [c_1-\sqrt [3]{-1} x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{a-\text {$\#$1}} \left (\frac {\text {$\#$1}-b}{a-b}\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};\frac {a-\text {$\#$1}}{a-b}\right )}{(b-\text {$\#$1})^{2/3}}\& \right ]\left [c_1+(-1)^{2/3} x\right ]\right \}\right \} \]
Maple: cpu = 0.156 (sec), leaf count = 126 \[ \left \{ x-\int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt [3]{ \left ( { \it \_a}-a \right ) ^{2} \left ( -b+{\it \_a} \right ) ^{2}}}}{d{\it \_a} }-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!2\,{\frac {1}{ \left ( i \sqrt {3}-1 \right ) \sqrt [3]{ \left ( {\it \_a}-a \right ) ^{2} \left ( -b+{\it \_a} \right ) ^{2}}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-2\,{\frac {1}{ \left ( i\sqrt {3}+1 \right ) \sqrt [3]{ \left ( {\it \_a}-a \right ) ^{2} \left ( -b+{\it \_a} \right ) ^{2}}}}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =a,y \left ( x \right ) =b \right \} \]