\[ \boxed { \left ( ax \left ( y \left ( x \right ) \right ) ^{3}+c \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( b{x}^{3}y \left ( x \right ) +c \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.032004 (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 = 0.093 (sec), leaf count = 761 \[ \left \{ y \left ( x \right ) ={\frac {1}{3\,ax}\sqrt [3]{ \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}}}+{x \left ( -b{x}^{2}+2\,{\it \_C1} \right ) {\frac {1}{\sqrt [3]{ \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 }}}}},y \left ( x \right ) =-{\frac {1}{6\,ax}\sqrt [3]{ \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}}}-{\frac {x \left ( -b{x}^{2}+2\,{\it \_C1} \right ) }{2}{\frac {1}{\sqrt [3]{ \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}}}}}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{3\,ax}\sqrt [3]{ \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}}}-{x \left ( -b{x}^{2}+2\,{ \it \_C1} \right ) {\frac {1}{\sqrt [3]{ \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 ) ,y \left ( x \right ) =-{\frac {1}{6 \,ax}\sqrt [3]{ \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}}}-{\frac { x \left ( -b{x}^{2}+2\,{\it \_C1} \right ) }{2}{\frac {1}{\sqrt [3]{ \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}}}}}+{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{3\,ax}\sqrt [3]{ \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}}}-{x \left ( -b{x}^{2}+2\,{\it \_C1} \right ) {\frac {1}{\sqrt [3 ]{ \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 ) \right \} \]