\[ \text {Global$\grave { }$y}'(\text {Global$\grave { }$x}) \left (3 \text {Global$\grave { }$a} \text {Global$\grave { }$x} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2+2 \text {Global$\grave { }$a} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^3-\text {Global$\grave { }$b} \text {Global$\grave { }$x}^3+\text {Global$\grave { }$c} \text {Global$\grave { }$x}^2\right )-\text {Global$\grave { }$a} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^3+2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^3+3 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+\text {Global$\grave { }$c} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2=0 \] ✓ Mathematica : cpu = 0.0823304 (sec), leaf count = 537
\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\sqrt [3]{2} \left (3 c_1 \text {Global$\grave { }$a}+3 \text {Global$\grave { }$a} \text {Global$\grave { }$c} \text {Global$\grave { }$x}\right )}{3 \text {Global$\grave { }$a} \sqrt [3]{\sqrt {\left (27 c_1 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+27 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^3\right ){}^2+4 \left (3 c_1 \text {Global$\grave { }$a}+3 \text {Global$\grave { }$a} \text {Global$\grave { }$c} \text {Global$\grave { }$x}\right ){}^3}+27 c_1 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+27 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^3}}-\frac {\sqrt [3]{\sqrt {\left (27 c_1 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+27 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^3\right ){}^2+4 \left (3 c_1 \text {Global$\grave { }$a}+3 \text {Global$\grave { }$a} \text {Global$\grave { }$c} \text {Global$\grave { }$x}\right ){}^3}+27 c_1 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+27 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^3}}{3 \sqrt [3]{2} \text {Global$\grave { }$a}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (27 c_1 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+27 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^3\right ){}^2+4 \left (3 c_1 \text {Global$\grave { }$a}+3 \text {Global$\grave { }$a} \text {Global$\grave { }$c} \text {Global$\grave { }$x}\right ){}^3}+27 c_1 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+27 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^3}}{6 \sqrt [3]{2} \text {Global$\grave { }$a}}-\frac {\left (1+i \sqrt {3}\right ) \left (3 c_1 \text {Global$\grave { }$a}+3 \text {Global$\grave { }$a} \text {Global$\grave { }$c} \text {Global$\grave { }$x}\right )}{3\ 2^{2/3} \text {Global$\grave { }$a} \sqrt [3]{\sqrt {\left (27 c_1 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+27 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^3\right ){}^2+4 \left (3 c_1 \text {Global$\grave { }$a}+3 \text {Global$\grave { }$a} \text {Global$\grave { }$c} \text {Global$\grave { }$x}\right ){}^3}+27 c_1 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+27 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^3}}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (27 c_1 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+27 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^3\right ){}^2+4 \left (3 c_1 \text {Global$\grave { }$a}+3 \text {Global$\grave { }$a} \text {Global$\grave { }$c} \text {Global$\grave { }$x}\right ){}^3}+27 c_1 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+27 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^3}}{6 \sqrt [3]{2} \text {Global$\grave { }$a}}-\frac {\left (1-i \sqrt {3}\right ) \left (3 c_1 \text {Global$\grave { }$a}+3 \text {Global$\grave { }$a} \text {Global$\grave { }$c} \text {Global$\grave { }$x}\right )}{3\ 2^{2/3} \text {Global$\grave { }$a} \sqrt [3]{\sqrt {\left (27 c_1 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+27 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^3\right ){}^2+4 \left (3 c_1 \text {Global$\grave { }$a}+3 \text {Global$\grave { }$a} \text {Global$\grave { }$c} \text {Global$\grave { }$x}\right ){}^3}+27 c_1 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$x}+27 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}^3}}\right \}\right \}\]
✓ Maple : cpu = 0.221 (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 {-3\,{\frac {-27\,a{b}^{2}{x}^{6}+54\,{\it \_C1}\,ab{x}^{4}-4\,{c}^{3}{x}^{3}-27\,{{\it \_C1}}^{2}a{x}^{2}+12\,{\it \_C1}\,{c}^{2}{x}^{2}-12\,{{\it \_C1}}^{2}cx+4\,{{\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 {-3\,{\frac {-27\,a{b}^{2}{x}^{6}+54\,{\it \_C1}\,ab{x}^{4}-4\,{c}^{3}{x}^{3}-27\,{{\it \_C1}}^{2}a{x}^{2}+12\,{\it \_C1}\,{c}^{2}{x}^{2}-12\,{{\it \_C1}}^{2}cx+4\,{{\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 {-3\,{\frac {-27\,a{b}^{2}{x}^{6}+54\,{\it \_C1}\,ab{x}^{4}-4\,{c}^{3}{x}^{3}-27\,{{\it \_C1}}^{2}a{x}^{2}+12\,{\it \_C1}\,{c}^{2}{x}^{2}-12\,{{\it \_C1}}^{2}cx+4\,{{\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 {-3\,{\frac {-27\,a{b}^{2}{x}^{6}+54\,{\it \_C1}\,ab{x}^{4}-4\,{c}^{3}{x}^{3}-27\,{{\it \_C1}}^{2}a{x}^{2}+12\,{\it \_C1}\,{c}^{2}{x}^{2}-12\,{{\it \_C1}}^{2}cx+4\,{{\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 {-3\,{\frac {-27\,a{b}^{2}{x}^{6}+54\,{\it \_C1}\,ab{x}^{4}-4\,{c}^{3}{x}^{3}-27\,{{\it \_C1}}^{2}a{x}^{2}+12\,{\it \_C1}\,{c}^{2}{x}^{2}-12\,{{\it \_C1}}^{2}cx+4\,{{\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 {-3\,{\frac {-27\,a{b}^{2}{x}^{6}+54\,{\it \_C1}\,ab{x}^{4}-4\,{c}^{3}{x}^{3}-27\,{{\it \_C1}}^{2}a{x}^{2}+12\,{\it \_C1}\,{c}^{2}{x}^{2}-12\,{{\it \_C1}}^{2}cx+4\,{{\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 {-3\,{\frac {-27\,a{b}^{2}{x}^{6}+54\,{\it \_C1}\,ab{x}^{4}-4\,{c}^{3}{x}^{3}-27\,{{\it \_C1}}^{2}a{x}^{2}+12\,{\it \_C1}\,{c}^{2}{x}^{2}-12\,{{\it \_C1}}^{2}cx+4\,{{\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 {-3\,{\frac {-27\,a{b}^{2}{x}^{6}+54\,{\it \_C1}\,ab{x}^{4}-4\,{c}^{3}{x}^{3}-27\,{{\it \_C1}}^{2}a{x}^{2}+12\,{\it \_C1}\,{c}^{2}{x}^{2}-12\,{{\it \_C1}}^{2}cx+4\,{{\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 {-3\,{\frac {-27\,a{b}^{2}{x}^{6}+54\,{\it \_C1}\,ab{x}^{4}-4\,{c}^{3}{x}^{3}-27\,{{\it \_C1}}^{2}a{x}^{2}+12\,{\it \_C1}\,{c}^{2}{x}^{2}-12\,{{\it \_C1}}^{2}cx+4\,{{\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 {-3\,{\frac {-27\,a{b}^{2}{x}^{6}+54\,{\it \_C1}\,ab{x}^{4}-4\,{c}^{3}{x}^{3}-27\,{{\it \_C1}}^{2}a{x}^{2}+12\,{\it \_C1}\,{c}^{2}{x}^{2}-12\,{{\it \_C1}}^{2}cx+4\,{{\it \_C1}}^{3}}{a}}} \right ) {a}^{2}}}}} \right ) \right \} \]