\[ y'(x) \left (3 a x y(x)^2+2 a y(x)^3-b x^3+c x^2\right )-a y(x)^3+2 b x^3+3 b x^2 y(x)+c y(x)^2=0 \] ✓ Mathematica : cpu = 0.0903104 (sec), leaf count = 537
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{2} \left (3 a c x+3 a c_1\right )}{3 a \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 \left (3 a c x+3 a c_1\right ){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}-\frac {\sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 \left (3 a c x+3 a c_1\right ){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}{3 \sqrt [3]{2} a}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 \left (3 a c x+3 a c_1\right ){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}{6 \sqrt [3]{2} a}-\frac {\left (1+i \sqrt {3}\right ) \left (3 a c x+3 a c_1\right )}{3\ 2^{2/3} a \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 \left (3 a c x+3 a c_1\right ){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 \left (3 a c x+3 a c_1\right ){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}{6 \sqrt [3]{2} a}-\frac {\left (1-i \sqrt {3}\right ) \left (3 a c x+3 a c_1\right )}{3\ 2^{2/3} a \sqrt [3]{\sqrt {\left (27 a^2 b x^3+27 a^2 c_1 x\right ){}^2+4 \left (3 a c x+3 a c_1\right ){}^3}+27 a^2 b x^3+27 a^2 c_1 x}}\right \}\right \}\]
✓ Maple : cpu = 0.218 (sec), leaf count = 912
\[ \left \{ y \left ( x \right ) ={\frac {1}{6\,a}\sqrt [3]{ \left ( -108\,b{x}^{3}+108\,{\it \_C1}\,x+12\,\sqrt {-{\frac {-81\,a{b}^{2}{x}^{6}+162\,{\it \_C1}\,ab{x}^{4}-12\,{c}^{3}{x}^{3}-81\,{{\it \_C1}}^{2}a{x}^{2}+36\,{\it \_C1}\,{c}^{2}{x}^{2}-36\,{{\it \_C1}}^{2}cx+12\,{{\it \_C1}}^{3}}{a}}} \right ) {a}^{2}}}+2\,{(-cx+{\it \_C1}){\frac {1}{\sqrt [3]{ \left ( -108\,b{x}^{3}+108\,{\it \_C1}\,x+12\,\sqrt {-{\frac {-81\,a{b}^{2}{x}^{6}+162\,{\it \_C1}\,ab{x}^{4}-12\,{c}^{3}{x}^{3}-81\,{{\it \_C1}}^{2}a{x}^{2}+36\,{\it \_C1}\,{c}^{2}{x}^{2}-36\,{{\it \_C1}}^{2}cx+12\,{{\it \_C1}}^{3}}{a}}} \right ) {a}^{2}}}}},y \left ( x \right ) =-{\frac {1}{12\,a}\sqrt [3]{ \left ( -108\,b{x}^{3}+108\,{\it \_C1}\,x+12\,\sqrt {-{\frac {-81\,a{b}^{2}{x}^{6}+162\,{\it \_C1}\,ab{x}^{4}-12\,{c}^{3}{x}^{3}-81\,{{\it \_C1}}^{2}a{x}^{2}+36\,{\it \_C1}\,{c}^{2}{x}^{2}-36\,{{\it \_C1}}^{2}cx+12\,{{\it \_C1}}^{3}}{a}}} \right ) {a}^{2}}}-{(-cx+{\it \_C1}){\frac {1}{\sqrt [3]{ \left ( -108\,b{x}^{3}+108\,{\it \_C1}\,x+12\,\sqrt {-{\frac {-81\,a{b}^{2}{x}^{6}+162\,{\it \_C1}\,ab{x}^{4}-12\,{c}^{3}{x}^{3}-81\,{{\it \_C1}}^{2}a{x}^{2}+36\,{\it \_C1}\,{c}^{2}{x}^{2}-36\,{{\it \_C1}}^{2}cx+12\,{{\it \_C1}}^{3}}{a}}} \right ) {a}^{2}}}}}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{6\,a}\sqrt [3]{ \left ( -108\,b{x}^{3}+108\,{\it \_C1}\,x+12\,\sqrt {-{\frac {-81\,a{b}^{2}{x}^{6}+162\,{\it \_C1}\,ab{x}^{4}-12\,{c}^{3}{x}^{3}-81\,{{\it \_C1}}^{2}a{x}^{2}+36\,{\it \_C1}\,{c}^{2}{x}^{2}-36\,{{\it \_C1}}^{2}cx+12\,{{\it \_C1}}^{3}}{a}}} \right ) {a}^{2}}}-2\,{(-cx+{\it \_C1}){\frac {1}{\sqrt [3]{ \left ( -108\,b{x}^{3}+108\,{\it \_C1}\,x+12\,\sqrt {-{\frac {-81\,a{b}^{2}{x}^{6}+162\,{\it \_C1}\,ab{x}^{4}-12\,{c}^{3}{x}^{3}-81\,{{\it \_C1}}^{2}a{x}^{2}+36\,{\it \_C1}\,{c}^{2}{x}^{2}-36\,{{\it \_C1}}^{2}cx+12\,{{\it \_C1}}^{3}}{a}}} \right ) {a}^{2}}}}} \right ) ,y \left ( x \right ) =-{\frac {1}{12\,a}\sqrt [3]{ \left ( -108\,b{x}^{3}+108\,{\it \_C1}\,x+12\,\sqrt {-{\frac {-81\,a{b}^{2}{x}^{6}+162\,{\it \_C1}\,ab{x}^{4}-12\,{c}^{3}{x}^{3}-81\,{{\it \_C1}}^{2}a{x}^{2}+36\,{\it \_C1}\,{c}^{2}{x}^{2}-36\,{{\it \_C1}}^{2}cx+12\,{{\it \_C1}}^{3}}{a}}} \right ) {a}^{2}}}-{(-cx+{\it \_C1}){\frac {1}{\sqrt [3]{ \left ( -108\,b{x}^{3}+108\,{\it \_C1}\,x+12\,\sqrt {-{\frac {-81\,a{b}^{2}{x}^{6}+162\,{\it \_C1}\,ab{x}^{4}-12\,{c}^{3}{x}^{3}-81\,{{\it \_C1}}^{2}a{x}^{2}+36\,{\it \_C1}\,{c}^{2}{x}^{2}-36\,{{\it \_C1}}^{2}cx+12\,{{\it \_C1}}^{3}}{a}}} \right ) {a}^{2}}}}}+{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{6\,a}\sqrt [3]{ \left ( -108\,b{x}^{3}+108\,{\it \_C1}\,x+12\,\sqrt {-{\frac {-81\,a{b}^{2}{x}^{6}+162\,{\it \_C1}\,ab{x}^{4}-12\,{c}^{3}{x}^{3}-81\,{{\it \_C1}}^{2}a{x}^{2}+36\,{\it \_C1}\,{c}^{2}{x}^{2}-36\,{{\it \_C1}}^{2}cx+12\,{{\it \_C1}}^{3}}{a}}} \right ) {a}^{2}}}-2\,{(-cx+{\it \_C1}){\frac {1}{\sqrt [3]{ \left ( -108\,b{x}^{3}+108\,{\it \_C1}\,x+12\,\sqrt {-{\frac {-81\,a{b}^{2}{x}^{6}+162\,{\it \_C1}\,ab{x}^{4}-12\,{c}^{3}{x}^{3}-81\,{{\it \_C1}}^{2}a{x}^{2}+36\,{\it \_C1}\,{c}^{2}{x}^{2}-36\,{{\it \_C1}}^{2}cx+12\,{{\it \_C1}}^{3}}{a}}} \right ) {a}^{2}}}}} \right ) \right \} \]