\[ y'(x)^3-f(x) \left (a y(x)^2+b y(x)+c\right )^2=0 \] ✓ Mathematica : cpu = 0.597848 (sec), leaf count = 353
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {\sqrt [3]{2} (2 \text {$\#$1} a+b) \left (\frac {a (\text {$\#$1} (\text {$\#$1} a+b)+c)}{4 a c-b^2}\right )^{2/3} \, _2F_1\left (\frac {1}{2},\frac {2}{3};\frac {3}{2};\frac {(b+2 a \text {$\#$1})^2}{b^2-4 a c}\right )}{a (\text {$\#$1} (\text {$\#$1} a+b)+c)^{2/3}}\& \right ]\left [\int _1^x\sqrt [3]{f(K[1])}dK[1]+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {\sqrt [3]{2} (2 \text {$\#$1} a+b) \left (\frac {a (\text {$\#$1} (\text {$\#$1} a+b)+c)}{4 a c-b^2}\right )^{2/3} \, _2F_1\left (\frac {1}{2},\frac {2}{3};\frac {3}{2};\frac {(b+2 a \text {$\#$1})^2}{b^2-4 a c}\right )}{a (\text {$\#$1} (\text {$\#$1} a+b)+c)^{2/3}}\& \right ]\left [\int _1^x-\sqrt [3]{-1} \sqrt [3]{f(K[2])}dK[2]+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {\sqrt [3]{2} (2 \text {$\#$1} a+b) \left (\frac {a (\text {$\#$1} (\text {$\#$1} a+b)+c)}{4 a c-b^2}\right )^{2/3} \, _2F_1\left (\frac {1}{2},\frac {2}{3};\frac {3}{2};\frac {(b+2 a \text {$\#$1})^2}{b^2-4 a c}\right )}{a (\text {$\#$1} (\text {$\#$1} a+b)+c)^{2/3}}\& \right ]\left [\int _1^x(-1)^{2/3} \sqrt [3]{f(K[3])}dK[3]+c_1\right ]\right \}\right \}\] ✓ Maple : cpu = 0.598 (sec), leaf count = 197
\[\int _{}^{y \relax (x )}\frac {1}{\left (\textit {\_a}^{2} a +\textit {\_a} b +c \right )^{\frac {2}{3}}}d \textit {\_a} +\int _{}^{x}-\frac {\left (f \left (\textit {\_a} \right ) \left (a y \relax (x )^{2}+b y \relax (x )+c \right )^{2}\right )^{\frac {1}{3}}}{\left (a y \relax (x )^{2}+b y \relax (x )+c \right )^{\frac {2}{3}}}d \textit {\_a} +c_{1} = 0\]