\[ y'(x) \left (3 a x y(x)^2+2 a y(x)^3-b x^3+c x^2\right )-a y(x)^3+2 b x^3+3 b x^2 y(x)+c y(x)^2=0 \] ✓ Mathematica : cpu = 0.391069 (sec), leaf count = 537
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{2} (3 a c x+3 a c_1)}{3 a \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 (3 a c x+3 a c_1){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}-\frac {\sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 (3 a c x+3 a c_1){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}{3 \sqrt [3]{2} a}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 (3 a c x+3 a c_1){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}{6 \sqrt [3]{2} a}-\frac {\left (1+i \sqrt {3}\right ) (3 a c x+3 a c_1)}{3\ 2^{2/3} a \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 (3 a c x+3 a c_1){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 (3 a c x+3 a c_1){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}{6 \sqrt [3]{2} a}-\frac {\left (1-i \sqrt {3}\right ) (3 a c x+3 a c_1)}{3\ 2^{2/3} a \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 (3 a c x+3 a c_1){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}\right \}\right \}\] ✓ Maple : cpu = 0.202 (sec), leaf count = 748
\[\left \{y \left (x \right ) = \frac {\left (-12 c x +12 c_{1}\right ) a +\left (\left (-108 b \,x^{3}+108 c_{1} x +12 \sqrt {\frac {81 a \,b^{2} x^{6}-162 c_{1} a b \,x^{4}+12 c^{3} x^{3}+81 c_{1}^{2} a \,x^{2}-36 c_{1} c^{2} x^{2}+36 c_{1}^{2} c x -12 c_{1}^{3}}{a}}\right ) a^{2}\right )^{\frac {2}{3}}}{6 \left (\left (-108 b \,x^{3}+108 c_{1} x +12 \sqrt {\frac {81 a \,b^{2} x^{6}-162 c_{1} a b \,x^{4}+12 c^{3} x^{3}+81 c_{1}^{2} a \,x^{2}-36 c_{1} c^{2} x^{2}+36 c_{1}^{2} c x -12 c_{1}^{3}}{a}}\right ) a^{2}\right )^{\frac {1}{3}} a}, y \left (x \right ) = -\frac {\left (-12 c x +12 c_{1}\right ) a +\left (\left (12 i c x -12 i c_{1}\right ) a +i \left (\left (-108 b \,x^{3}+108 c_{1} x +12 \sqrt {\frac {81 a \,b^{2} x^{6}-162 c_{1} a b \,x^{4}+12 c^{3} x^{3}+81 c_{1}^{2} a \,x^{2}-36 c_{1} c^{2} x^{2}+36 c_{1}^{2} c x -12 c_{1}^{3}}{a}}\right ) a^{2}\right )^{\frac {2}{3}}\right ) \sqrt {3}+\left (\left (-108 b \,x^{3}+108 c_{1} x +12 \sqrt {\frac {81 a \,b^{2} x^{6}-162 c_{1} a b \,x^{4}+12 c^{3} x^{3}+81 c_{1}^{2} a \,x^{2}-36 c_{1} c^{2} x^{2}+36 c_{1}^{2} c x -12 c_{1}^{3}}{a}}\right ) a^{2}\right )^{\frac {2}{3}}}{12 \left (\left (-108 b \,x^{3}+108 c_{1} x +12 \sqrt {\frac {81 a \,b^{2} x^{6}-162 c_{1} a b \,x^{4}+12 c^{3} x^{3}+81 c_{1}^{2} a \,x^{2}-36 c_{1} c^{2} x^{2}+36 c_{1}^{2} c x -12 c_{1}^{3}}{a}}\right ) a^{2}\right )^{\frac {1}{3}} a}, y \left (x \right ) = \frac {\left (12 c x -12 c_{1}\right ) a +\left (\left (12 i c x -12 i c_{1}\right ) a +i \left (\left (-108 b \,x^{3}+108 c_{1} x +12 \sqrt {\frac {81 a \,b^{2} x^{6}-162 c_{1} a b \,x^{4}+12 c^{3} x^{3}+81 c_{1}^{2} a \,x^{2}-36 c_{1} c^{2} x^{2}+36 c_{1}^{2} c x -12 c_{1}^{3}}{a}}\right ) a^{2}\right )^{\frac {2}{3}}\right ) \sqrt {3}-\left (\left (-108 b \,x^{3}+108 c_{1} x +12 \sqrt {\frac {81 a \,b^{2} x^{6}-162 c_{1} a b \,x^{4}+12 c^{3} x^{3}+81 c_{1}^{2} a \,x^{2}-36 c_{1} c^{2} x^{2}+36 c_{1}^{2} c x -12 c_{1}^{3}}{a}}\right ) a^{2}\right )^{\frac {2}{3}}}{12 \left (\left (-108 b \,x^{3}+108 c_{1} x +12 \sqrt {\frac {81 a \,b^{2} x^{6}-162 c_{1} a b \,x^{4}+12 c^{3} x^{3}+81 c_{1}^{2} a \,x^{2}-36 c_{1} c^{2} x^{2}+36 c_{1}^{2} c x -12 c_{1}^{3}}{a}}\right ) a^{2}\right )^{\frac {1}{3}} a}\right \}\]