\[ x y'(x) \left (a x y(x)^3+c\right )+y(x) \left (b x^3 y(x)+c\right )=0 \] ✓ Mathematica : cpu = 0.050313 (sec), leaf count = 484
\[\left \{\left \{y(x)\to \frac {x \left (2 c_1-b x^2\right )}{\sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {a^3 x^4 \left (27 a c^2+x^2 \left (b x^2-2 c_1\right ){}^3\right )}+9 a^2 c x^2}}+\frac {\sqrt [3]{\sqrt {3} \sqrt {a^3 x^4 \left (27 a c^2+x^2 \left (b x^2-2 c_1\right ){}^3\right )}+9 a^2 c x^2}}{3^{2/3} a x}\right \},\left \{y(x)\to \frac {i \sqrt [3]{3} \left (\sqrt {3}+i\right ) \left (\sqrt {3} \sqrt {a^3 x^4 \left (27 a c^2+x^2 \left (b x^2-2 c_1\right ){}^3\right )}+9 a^2 c x^2\right ){}^{2/3}+\sqrt [6]{3} \left (\sqrt {3}+3 i\right ) a x^2 \left (b x^2-2 c_1\right )}{6 a x \sqrt [3]{\sqrt {3} \sqrt {a^3 x^4 \left (27 a c^2+x^2 \left (b x^2-2 c_1\right ){}^3\right )}+9 a^2 c x^2}}\right \},\left \{y(x)\to \frac {\sqrt [6]{3} \left (\sqrt {3}-3 i\right ) a x^2 \left (b x^2-2 c_1\right )-i \sqrt [3]{3} \left (\sqrt {3}-i\right ) \left (\sqrt {3} \sqrt {a^3 x^4 \left (27 a c^2+x^2 \left (b x^2-2 c_1\right ){}^3\right )}+9 a^2 c x^2\right ){}^{2/3}}{6 a x \sqrt [3]{\sqrt {3} \sqrt {a^3 x^4 \left (27 a c^2+x^2 \left (b x^2-2 c_1\right ){}^3\right )}+9 a^2 c x^2}}\right \}\right \}\]
✓ Maple : cpu = 0.143 (sec), leaf count = 630
\[ \left \{ y \left ( x \right ) =-{\frac {{3}^{{\frac {2}{3}}}}{18\,ax} \left ( \left ( 3\,i \left ( b{x}^{2}-2\,{\it \_C1} \right ) {x}^{2}a+i \left ( \left ( 27\,c+3\,\sqrt {{\frac {3\,{b}^{3}{x}^{8}-18\,{\it \_C1}\,{b}^{2}{x}^{6}+36\,{{\it \_C1}}^{2}b{x}^{4}-24\,{{\it \_C1}}^{3}{x}^{2}+81\,{c}^{2}a}{a}}} \right ) {a}^{2}{x}^{2} \right ) ^{{\frac {2}{3}}} \right ) \sqrt {3}+ \left ( -3\,{x}^{4}b+6\,{x}^{2}{\it \_C1} \right ) a+ \left ( \left ( 27\,c+3\,\sqrt {{\frac {3\,{b}^{3}{x}^{8}-18\,{\it \_C1}\,{b}^{2}{x}^{6}+36\,{{\it \_C1}}^{2}b{x}^{4}-24\,{{\it \_C1}}^{3}{x}^{2}+81\,{c}^{2}a}{a}}} \right ) {a}^{2}{x}^{2} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{ \left ( 9\,c+\sqrt {{\frac {3\,{b}^{3}{x}^{8}-18\,{\it \_C1}\,{b}^{2}{x}^{6}+36\,{{\it \_C1}}^{2}b{x}^{4}-24\,{{\it \_C1}}^{3}{x}^{2}+81\,{c}^{2}a}{a}}} \right ) {a}^{2}{x}^{2}}}}},y \left ( x \right ) ={\frac {{3}^{{\frac {2}{3}}}}{18\,ax} \left ( \left ( 3\,i \left ( b{x}^{2}-2\,{\it \_C1} \right ) {x}^{2}a+i \left ( \left ( 27\,c+3\,\sqrt {{\frac {3\,{b}^{3}{x}^{8}-18\,{\it \_C1}\,{b}^{2}{x}^{6}+36\,{{\it \_C1}}^{2}b{x}^{4}-24\,{{\it \_C1}}^{3}{x}^{2}+81\,{c}^{2}a}{a}}} \right ) {a}^{2}{x}^{2} \right ) ^{{\frac {2}{3}}} \right ) \sqrt {3}+ \left ( 3\,{x}^{4}b-6\,{x}^{2}{\it \_C1} \right ) a- \left ( \left ( 27\,c+3\,\sqrt {{\frac {3\,{b}^{3}{x}^{8}-18\,{\it \_C1}\,{b}^{2}{x}^{6}+36\,{{\it \_C1}}^{2}b{x}^{4}-24\,{{\it \_C1}}^{3}{x}^{2}+81\,{c}^{2}a}{a}}} \right ) {a}^{2}{x}^{2} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{ \left ( 9\,c+\sqrt {{\frac {3\,{b}^{3}{x}^{8}-18\,{\it \_C1}\,{b}^{2}{x}^{6}+36\,{{\it \_C1}}^{2}b{x}^{4}-24\,{{\it \_C1}}^{3}{x}^{2}+81\,{c}^{2}a}{a}}} \right ) {a}^{2}{x}^{2}}}}},y \left ( x \right ) ={\frac {{3}^{{\frac {2}{3}}}}{9\,ax} \left ( -3\,ab{x}^{4}+6\,{\it \_C1}\,a{x}^{2}+ \left ( \left ( 27\,c+3\,\sqrt {{\frac {3\,{b}^{3}{x}^{8}-18\,{\it \_C1}\,{b}^{2}{x}^{6}+36\,{{\it \_C1}}^{2}b{x}^{4}-24\,{{\it \_C1}}^{3}{x}^{2}+81\,{c}^{2}a}{a}}} \right ) {a}^{2}{x}^{2} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{ \left ( 9\,c+\sqrt {{\frac {3\,{b}^{3}{x}^{8}-18\,{\it \_C1}\,{b}^{2}{x}^{6}+36\,{{\it \_C1}}^{2}b{x}^{4}-24\,{{\it \_C1}}^{3}{x}^{2}+81\,{c}^{2}a}{a}}} \right ) {a}^{2}{x}^{2}}}}} \right \} \]