\[ \text {Global$\grave { }$x} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x}) \left (\text {Global$\grave { }$a} \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^3+\text {Global$\grave { }$c}\right )+\text {Global$\grave { }$y}(\text {Global$\grave { }$x}) \left (\text {Global$\grave { }$b} \text {Global$\grave { }$x}^3 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+\text {Global$\grave { }$c}\right )=0 \] ✓ Mathematica : cpu = 0.0491124 (sec), leaf count = 463
\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\sqrt [3]{\sqrt {108 \text {Global$\grave { }$a}^3 \text {Global$\grave { }$x}^3 \left (\text {Global$\grave { }$b} \text {Global$\grave { }$x}^3-2 c_1 \text {Global$\grave { }$x}\right ){}^3+2916 \text {Global$\grave { }$a}^4 \text {Global$\grave { }$c}^2 \text {Global$\grave { }$x}^4}+54 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$c} \text {Global$\grave { }$x}^2}}{3 \sqrt [3]{2} \text {Global$\grave { }$a} \text {Global$\grave { }$x}}-\frac {\sqrt [3]{2} \left (\text {Global$\grave { }$b} \text {Global$\grave { }$x}^3-2 c_1 \text {Global$\grave { }$x}\right )}{\sqrt [3]{\sqrt {108 \text {Global$\grave { }$a}^3 \text {Global$\grave { }$x}^3 \left (\text {Global$\grave { }$b} \text {Global$\grave { }$x}^3-2 c_1 \text {Global$\grave { }$x}\right ){}^3+2916 \text {Global$\grave { }$a}^4 \text {Global$\grave { }$c}^2 \text {Global$\grave { }$x}^4}+54 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$c} \text {Global$\grave { }$x}^2}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\left (1+i \sqrt {3}\right ) \left (\text {Global$\grave { }$b} \text {Global$\grave { }$x}^3-2 c_1 \text {Global$\grave { }$x}\right )}{2^{2/3} \sqrt [3]{\sqrt {108 \text {Global$\grave { }$a}^3 \text {Global$\grave { }$x}^3 \left (\text {Global$\grave { }$b} \text {Global$\grave { }$x}^3-2 c_1 \text {Global$\grave { }$x}\right ){}^3+2916 \text {Global$\grave { }$a}^4 \text {Global$\grave { }$c}^2 \text {Global$\grave { }$x}^4}+54 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$c} \text {Global$\grave { }$x}^2}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {108 \text {Global$\grave { }$a}^3 \text {Global$\grave { }$x}^3 \left (\text {Global$\grave { }$b} \text {Global$\grave { }$x}^3-2 c_1 \text {Global$\grave { }$x}\right ){}^3+2916 \text {Global$\grave { }$a}^4 \text {Global$\grave { }$c}^2 \text {Global$\grave { }$x}^4}+54 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$c} \text {Global$\grave { }$x}^2}}{6 \sqrt [3]{2} \text {Global$\grave { }$a} \text {Global$\grave { }$x}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\left (1-i \sqrt {3}\right ) \left (\text {Global$\grave { }$b} \text {Global$\grave { }$x}^3-2 c_1 \text {Global$\grave { }$x}\right )}{2^{2/3} \sqrt [3]{\sqrt {108 \text {Global$\grave { }$a}^3 \text {Global$\grave { }$x}^3 \left (\text {Global$\grave { }$b} \text {Global$\grave { }$x}^3-2 c_1 \text {Global$\grave { }$x}\right ){}^3+2916 \text {Global$\grave { }$a}^4 \text {Global$\grave { }$c}^2 \text {Global$\grave { }$x}^4}+54 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$c} \text {Global$\grave { }$x}^2}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {108 \text {Global$\grave { }$a}^3 \text {Global$\grave { }$x}^3 \left (\text {Global$\grave { }$b} \text {Global$\grave { }$x}^3-2 c_1 \text {Global$\grave { }$x}\right ){}^3+2916 \text {Global$\grave { }$a}^4 \text {Global$\grave { }$c}^2 \text {Global$\grave { }$x}^4}+54 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$c} \text {Global$\grave { }$x}^2}}{6 \sqrt [3]{2} \text {Global$\grave { }$a} \text {Global$\grave { }$x}}\right \}\right \}\]
✓ Maple : cpu = 0.134 (sec), leaf count = 761
\[ \left \{ y \left ( x \right ) ={\frac {1}{3\,ax}\sqrt [3]{ \left ( 27\,c+3\,\sqrt {-3\,{\frac {-{b}^{3}{x}^{8}+6\,{\it \_C1}\,{b}^{2}{x}^{6}-12\,{{\it \_C1}}^{2}b{x}^{4}+8\,{{\it \_C1}}^{3}{x}^{2}-27\,{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 {-3\,{\frac {-{b}^{3}{x}^{8}+6\,{\it \_C1}\,{b}^{2}{x}^{6}-12\,{{\it \_C1}}^{2}b{x}^{4}+8\,{{\it \_C1}}^{3}{x}^{2}-27\,{c}^{2}a}{a}}} \right ) {a}^{2}{x}^{2}}}}},y \left ( x \right ) =-{\frac {1}{6\,ax}\sqrt [3]{ \left ( 27\,c+3\,\sqrt {-3\,{\frac {-{b}^{3}{x}^{8}+6\,{\it \_C1}\,{b}^{2}{x}^{6}-12\,{{\it \_C1}}^{2}b{x}^{4}+8\,{{\it \_C1}}^{3}{x}^{2}-27\,{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 {-3\,{\frac {-{b}^{3}{x}^{8}+6\,{\it \_C1}\,{b}^{2}{x}^{6}-12\,{{\it \_C1}}^{2}b{x}^{4}+8\,{{\it \_C1}}^{3}{x}^{2}-27\,{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 {-3\,{\frac {-{b}^{3}{x}^{8}+6\,{\it \_C1}\,{b}^{2}{x}^{6}-12\,{{\it \_C1}}^{2}b{x}^{4}+8\,{{\it \_C1}}^{3}{x}^{2}-27\,{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 {-3\,{\frac {-{b}^{3}{x}^{8}+6\,{\it \_C1}\,{b}^{2}{x}^{6}-12\,{{\it \_C1}}^{2}b{x}^{4}+8\,{{\it \_C1}}^{3}{x}^{2}-27\,{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 {-3\,{\frac {-{b}^{3}{x}^{8}+6\,{\it \_C1}\,{b}^{2}{x}^{6}-12\,{{\it \_C1}}^{2}b{x}^{4}+8\,{{\it \_C1}}^{3}{x}^{2}-27\,{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 {-3\,{\frac {-{b}^{3}{x}^{8}+6\,{\it \_C1}\,{b}^{2}{x}^{6}-12\,{{\it \_C1}}^{2}b{x}^{4}+8\,{{\it \_C1}}^{3}{x}^{2}-27\,{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 {-3\,{\frac {-{b}^{3}{x}^{8}+6\,{\it \_C1}\,{b}^{2}{x}^{6}-12\,{{\it \_C1}}^{2}b{x}^{4}+8\,{{\it \_C1}}^{3}{x}^{2}-27\,{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 {-3\,{\frac {-{b}^{3}{x}^{8}+6\,{\it \_C1}\,{b}^{2}{x}^{6}-12\,{{\it \_C1}}^{2}b{x}^{4}+8\,{{\it \_C1}}^{3}{x}^{2}-27\,{c}^{2}a}{a}}} \right ) {a}^{2}{x}^{2}}}}} \right ) \right \} \]