\[ a \sqrt [3]{y'(x)^3+1}+b x y'(x)-y(x)=0 \] ✓ Mathematica : cpu = 430.306 (sec), leaf count = 119
\[\text {Solve}\left [\left \{x=\frac {a (b-1) \text {K$\$$6270}^3 (\text {K$\$$6270}-b \text {K$\$$6270})^{\frac {b}{1-b}+\frac {1}{b-1}} \, _2F_1\left (\frac {2}{3},\frac {2-3 b}{3-3 b};\frac {5-6 b}{3-3 b};-\text {K$\$$6270}^3\right )}{3 b-2}+c_1 (\text {K$\$$6270}-b \text {K$\$$6270})^{\frac {b}{1-b}},y(x)=a \sqrt [3]{\text {K$\$$6270}^3+1}+b \text {K$\$$6270} x\right \},\{y(x),\text {K$\$$6270}\}\right ]\]
✓ Maple : cpu = 0.135 (sec), leaf count = 3961
\[ \left \{ x- \left ( {\frac {1}{2\,{b}^{3}{x}^{3}+2\,{a}^{3}} \left ( 2\,{b}^{2}{x}^{2}y \left ( x \right ) \sqrt [3]{-4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}}-4\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}bx+a \left ( -4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{-4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}}}}} \right ) ^{-{\frac {b}{b-1}}} \left ( \int ^{{\frac {1}{2\,{b}^{3}{x}^{3}+2\,{a}^{3}} \left ( 2\,{b}^{2}{x}^{2}y \left ( x \right ) \sqrt [3]{-4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}}-4\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}bx+a \left ( -4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{-4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}}}}}}\!-{\frac {a}{b-1}{{\it \_a}}^{1+{\frac {b}{b-1}}} \left ( {{\it \_a}}^{3}+1 \right ) ^{-{\frac {2}{3}}}}{d{\it \_a}}+{\it \_C1} \right ) =0,x- \left ( -{\frac {1}{4\,{b}^{3}{x}^{3}+4\,{a}^{3}} \left ( 4\,i\sqrt {3}{a}^{2}bx \left ( y \left ( x \right ) \right ) ^{2}-4\,{b}^{2}{x}^{2}y \left ( x \right ) \sqrt [3]{-4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}}-4\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}bx+i \left ( -4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}} \right ) ^{{\frac {2}{3}}}\sqrt {3}a+a \left ( -4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{-4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}}}}} \right ) ^{-{\frac {b}{b-1}}} \left ( \int ^{-{\frac {1}{4\,{b}^{3}{x}^{3}+4\,{a}^{3}} \left ( 4\,i\sqrt {3}{a}^{2}bx \left ( y \left ( x \right ) \right ) ^{2}-4\,{b}^{2}{x}^{2}y \left ( x \right ) \sqrt [3]{-4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}}-4\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}bx+i \left ( -4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}} \right ) ^{{\frac {2}{3}}}\sqrt {3}a+a \left ( -4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{-4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}}}}}}\!-{\frac {a}{b-1}{{\it \_a}}^{1+{\frac {b}{b-1}}} \left ( {{\it \_a}}^{3}+1 \right ) ^{-{\frac {2}{3}}}}{d{\it \_a}}+{\it \_C1} \right ) =0,x- \left ( {\frac {1}{4\,{b}^{3}{x}^{3}+4\,{a}^{3}} \left ( 4\,i\sqrt {3}{a}^{2}bx \left ( y \left ( x \right ) \right ) ^{2}+4\,{b}^{2}{x}^{2}y \left ( x \right ) \sqrt [3]{-4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}}+4\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}bx+i \left ( -4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}} \right ) ^{{\frac {2}{3}}}\sqrt {3}a-a \left ( -4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{-4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}}}}} \right ) ^{-{\frac {b}{b-1}}} \left ( \int ^{{\frac {1}{4\,{b}^{3}{x}^{3}+4\,{a}^{3}} \left ( 4\,i\sqrt {3}{a}^{2}bx \left ( y \left ( x \right ) \right ) ^{2}+4\,{b}^{2}{x}^{2}y \left ( x \right ) \sqrt [3]{-4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}}+4\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}bx+i \left ( -4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}} \right ) ^{{\frac {2}{3}}}\sqrt {3}a-a \left ( -4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{-4\,{b}^{6}{x}^{6}-8\,{a}^{3}{b}^{3}{x}^{3}-4\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}{b}^{3}{x}^{3}-4\,{a}^{6}+4\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+4\,{a}^{3}\sqrt {{b}^{6}{x}^{6}+2\,{a}^{3}{b}^{3}{x}^{3}+2\,{b}^{3}{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+{a}^{6}-2\, \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{6}}}}}}}\!-{\frac {a}{b-1}{{\it \_a}}^{1+{\frac {b}{b-1}}} \left ( {{\it \_a}}^{3}+1 \right ) ^{-{\frac {2}{3}}}}{d{\it \_a}}+{\it \_C1} \right ) =0 \right \} \]