\[ x y'(x) \left (a x y(x)^3+c\right )+y(x) \left (b x^3 y(x)+c\right )=0 \] ✓ Mathematica : cpu = 0.277495 (sec), leaf count = 463
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{54 a^2 c x^2+\sqrt {2916 a^4 c^2 x^4+108 a^3 x^3 \left (b x^3-2 c_1 x\right ){}^3}}}{3 \sqrt [3]{2} a x}-\frac {\sqrt [3]{2} \left (b x^3-2 c_1 x\right )}{\sqrt [3]{54 a^2 c x^2+\sqrt {2916 a^4 c^2 x^4+108 a^3 x^3 \left (b x^3-2 c_1 x\right ){}^3}}}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \left (b x^3-2 c_1 x\right )}{2^{2/3} \sqrt [3]{54 a^2 c x^2+\sqrt {2916 a^4 c^2 x^4+108 a^3 x^3 \left (b x^3-2 c_1 x\right ){}^3}}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{54 a^2 c x^2+\sqrt {2916 a^4 c^2 x^4+108 a^3 x^3 \left (b x^3-2 c_1 x\right ){}^3}}}{6 \sqrt [3]{2} a x}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \left (b x^3-2 c_1 x\right )}{2^{2/3} \sqrt [3]{54 a^2 c x^2+\sqrt {2916 a^4 c^2 x^4+108 a^3 x^3 \left (b x^3-2 c_1 x\right ){}^3}}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{54 a^2 c x^2+\sqrt {2916 a^4 c^2 x^4+108 a^3 x^3 \left (b x^3-2 c_1 x\right ){}^3}}}{6 \sqrt [3]{2} a x}\right \}\right \}\] ✓ Maple : cpu = 0.116 (sec), leaf count = 630
\[\left \{y \left (x \right ) = \frac {3^{\frac {2}{3}} \left (\left (3 x^{4} b -6 c_{1} x^{2}\right ) a +\left (3 i \left (b \,x^{2}-2 c_{1}\right ) a \,x^{2}+i \left (\left (27 c +3 \sqrt {\frac {3 b^{3} x^{8}-18 c_{1} b^{2} x^{6}+36 c_{1}^{2} b \,x^{4}-24 c_{1}^{3} x^{2}+81 c^{2} a}{a}}\right ) a^{2} x^{2}\right )^{\frac {2}{3}}\right ) \sqrt {3}-\left (\left (27 c +3 \sqrt {\frac {3 b^{3} x^{8}-18 c_{1} b^{2} x^{6}+36 c_{1}^{2} b \,x^{4}-24 c_{1}^{3} x^{2}+81 c^{2} a}{a}}\right ) a^{2} x^{2}\right )^{\frac {2}{3}}\right )}{18 \left (\left (9 c +\sqrt {\frac {3 b^{3} x^{8}-18 c_{1} b^{2} x^{6}+36 c_{1}^{2} b \,x^{4}-24 c_{1}^{3} x^{2}+81 c^{2} a}{a}}\right ) a^{2} x^{2}\right )^{\frac {1}{3}} a x}, y \left (x \right ) = -\frac {\left (\left (-3 x^{4} b +6 c_{1} x^{2}\right ) a +\left (3 i \left (b \,x^{2}-2 c_{1}\right ) a \,x^{2}+i \left (\left (27 c +3 \sqrt {\frac {3 b^{3} x^{8}-18 c_{1} b^{2} x^{6}+36 c_{1}^{2} b \,x^{4}-24 c_{1}^{3} x^{2}+81 c^{2} a}{a}}\right ) a^{2} x^{2}\right )^{\frac {2}{3}}\right ) \sqrt {3}+\left (\left (27 c +3 \sqrt {\frac {3 b^{3} x^{8}-18 c_{1} b^{2} x^{6}+36 c_{1}^{2} b \,x^{4}-24 c_{1}^{3} x^{2}+81 c^{2} a}{a}}\right ) a^{2} x^{2}\right )^{\frac {2}{3}}\right ) 3^{\frac {2}{3}}}{18 \left (\left (9 c +\sqrt {\frac {3 b^{3} x^{8}-18 c_{1} b^{2} x^{6}+36 c_{1}^{2} b \,x^{4}-24 c_{1}^{3} x^{2}+81 c^{2} a}{a}}\right ) a^{2} x^{2}\right )^{\frac {1}{3}} a x}, y \left (x \right ) = \frac {\left (-3 a b \,x^{4}+6 c_{1} a \,x^{2}+\left (\left (27 c +3 \sqrt {\frac {3 b^{3} x^{8}-18 c_{1} b^{2} x^{6}+36 c_{1}^{2} b \,x^{4}-24 c_{1}^{3} x^{2}+81 c^{2} a}{a}}\right ) a^{2} x^{2}\right )^{\frac {2}{3}}\right ) 3^{\frac {2}{3}}}{9 \left (\left (9 c +\sqrt {\frac {3 b^{3} x^{8}-18 c_{1} b^{2} x^{6}+36 c_{1}^{2} b \,x^{4}-24 c_{1}^{3} x^{2}+81 c^{2} a}{a}}\right ) a^{2} x^{2}\right )^{\frac {1}{3}} a x}\right \}\]