\[ \boxed { a\sqrt [3]{ \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{3}+1}+bx{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) =0} \]
Mathematica: cpu = 264.371071 (sec), leaf count = 119 \[ \text {Solve}\left [\left \{x=\frac {a (b-1) \text {K$\$$1486420}^3 (\text {K$\$$1486420}-b \text {K$\$$1486420})^{\frac {b}{1-b}+\frac {1}{b-1}} \, _2F_1\left (\frac {2}{3},\frac {2-3 b}{3-3 b};\frac {5-6 b}{3-3 b};-\text {K$\$$1486420}^3\right )}{3 b-2}+c_1 (\text {K$\$$1486420}-b \text {K$\$$1486420})^{\frac {b}{1-b}},y(x)=a \sqrt [3]{\text {K$\$$1486420}^3+1}+b \text {K$\$$1486420} x\right \},\{y(x),\text {K$\$$1486420}\}\right ] \]
Maple: cpu = 0.094 (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 \sqrt {3} \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}}}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\sqrt {3} \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}}}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\sqrt {3} \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}}} 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\sqrt {3} \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}}}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 \} \]