\[ 2 \left (x y'(x)+y(x)\right )^3-y(x) y'(x)=0 \] ✗ Mathematica : cpu = 3599.93 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.943 (sec), leaf count = 3181
\[ \left \{ \int _{{\it \_b}}^{x}\!-{\frac {1}{{\it \_a}} \left ( {6}^{{\frac {2}{3}}} \left ( y \left ( x \right ) \left ( \sqrt {3}\sqrt {{\frac {y \left ( x \right ) \left ( 27\,{\it \_a}\,y \left ( x \right ) -2 \right ) }{{\it \_a}}}}-9\,y \left ( x \right ) \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}-6\,y \left ( x \right ) {\it \_a}\,\sqrt [3]{6}\sqrt [3]{y \left ( x \right ) \left ( \sqrt {3}\sqrt {{\frac {y \left ( x \right ) \left ( 27\,{\it \_a}\,y \left ( x \right ) -2 \right ) }{{\it \_a}}}}-9\,y \left ( x \right ) \right ) {{\it \_a}}^{2}}+6\,{\it \_a}\,y \left ( x \right ) \right ) \left ( {6}^{{\frac {2}{3}}} \left ( y \left ( x \right ) \left ( \sqrt {3}\sqrt {{\frac {y \left ( x \right ) \left ( 27\,{\it \_a}\,y \left ( x \right ) -2 \right ) }{{\it \_a}}}}-9\,y \left ( x \right ) \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}+6\,{\it \_a}\,y \left ( x \right ) \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!6\,{x\sqrt [3]{6}\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,x{\it \_f}-2 \right ) }{x}}}-9\,{\it \_f} \right ) {x}^{2}} \left ( {6}^{2/3} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,x{\it \_f}-2 \right ) }{x}}}-9\,{\it \_f} \right ) {x}^{2} \right ) ^{2/3}+6\,x{\it \_f} \right ) ^{-1}}-\int _{{\it \_b}}^{x}\!-{\frac {1}{{\it \_a}} \left ( {\frac {2\,{6}^{2/3}}{3} \left ( \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}+{\it \_f}\, \left ( {\frac {\sqrt {3}}{2} \left ( {\frac {27\,{\it \_a}\,{\it \_f}-2}{{\it \_a}}}+27\,{\it \_f} \right ) {\frac {1}{\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}}}}-9 \right ) {{\it \_a}}^{2} \right ) {\frac {1}{\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}}}}-6\,{\it \_a}\,\sqrt [3]{6}\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}-2\,{{\it \_a}\,{\it \_f}\,\sqrt [3]{6} \left ( \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}+{\it \_f}\, \left ( 1/2\,{\sqrt {3} \left ( {\frac {27\,{\it \_a}\,{\it \_f}-2}{{\it \_a}}}+27\,{\it \_f} \right ) {\frac {1}{\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}}}}-9 \right ) {{\it \_a}}^{2} \right ) \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{-2/3}}+6\,{\it \_a} \right ) \left ( {6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}+6\,{\it \_a}\,{\it \_f} \right ) ^{-1}}+{\frac {1}{{\it \_a}} \left ( {6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}-6\,{\it \_f}\,{\it \_a}\,\sqrt [3]{6}\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}+6\,{\it \_a}\,{\it \_f} \right ) \left ( {\frac {2\,{6}^{2/3}}{3} \left ( \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}+{\it \_f}\, \left ( {\frac {\sqrt {3}}{2} \left ( {\frac {27\,{\it \_a}\,{\it \_f}-2}{{\it \_a}}}+27\,{\it \_f} \right ) {\frac {1}{\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}}}}-9 \right ) {{\it \_a}}^{2} \right ) {\frac {1}{\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}}}}+6\,{\it \_a} \right ) \left ( {6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}+6\,{\it \_a}\,{\it \_f} \right ) ^{-2}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0,\int _{{\it \_b}}^{x}\!-{\frac {1}{{\it \_a}} \left ( i{6}^{{\frac {2}{3}}} \left ( y \left ( x \right ) \left ( \sqrt {3}\sqrt {{\frac {y \left ( x \right ) \left ( 27\,{\it \_a}\,y \left ( x \right ) -2 \right ) }{{\it \_a}}}}-9\,y \left ( x \right ) \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}\sqrt {3}+{6}^{{\frac {2}{3}}} \left ( y \left ( x \right ) \left ( \sqrt {3}\sqrt {{\frac {y \left ( x \right ) \left ( 27\,{\it \_a}\,y \left ( x \right ) -2 \right ) }{{\it \_a}}}}-9\,y \left ( x \right ) \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}+12\,y \left ( x \right ) {\it \_a}\,\sqrt [3]{6}\sqrt [3]{y \left ( x \right ) \left ( \sqrt {3}\sqrt {{\frac {y \left ( x \right ) \left ( 27\,{\it \_a}\,y \left ( x \right ) -2 \right ) }{{\it \_a}}}}-9\,y \left ( x \right ) \right ) {{\it \_a}}^{2}}-6\,i\sqrt {3}{\it \_a}\,y \left ( x \right ) +6\,{\it \_a}\,y \left ( x \right ) \right ) \left ( i{6}^{{\frac {2}{3}}} \left ( y \left ( x \right ) \left ( \sqrt {3}\sqrt {{\frac {y \left ( x \right ) \left ( 27\,{\it \_a}\,y \left ( x \right ) -2 \right ) }{{\it \_a}}}}-9\,y \left ( x \right ) \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}\sqrt {3}+{6}^{{\frac {2}{3}}} \left ( y \left ( x \right ) \left ( \sqrt {3}\sqrt {{\frac {y \left ( x \right ) \left ( 27\,{\it \_a}\,y \left ( x \right ) -2 \right ) }{{\it \_a}}}}-9\,y \left ( x \right ) \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}-6\,i\sqrt {3}{\it \_a}\,y \left ( x \right ) +6\,{\it \_a}\,y \left ( x \right ) \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!-12\,{x\sqrt [3]{6}\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,x{\it \_f}-2 \right ) }{x}}}-9\,{\it \_f} \right ) {x}^{2}} \left ( i{6}^{2/3} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,x{\it \_f}-2 \right ) }{x}}}-9\,{\it \_f} \right ) {x}^{2} \right ) ^{2/3}\sqrt {3}+{6}^{2/3} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,x{\it \_f}-2 \right ) }{x}}}-9\,{\it \_f} \right ) {x}^{2} \right ) ^{2/3}-6\,i\sqrt {3}x{\it \_f}+6\,x{\it \_f} \right ) ^{-1}}-\int _{{\it \_b}}^{x}\!-{\frac {1}{{\it \_a}} \left ( {{\frac {2\,i}{3}}{6}^{{\frac {2}{3}}}\sqrt {3} \left ( \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}+{\it \_f}\, \left ( {\frac {\sqrt {3}}{2} \left ( {\frac {27\,{\it \_a}\,{\it \_f}-2}{{\it \_a}}}+27\,{\it \_f} \right ) {\frac {1}{\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}}}}-9 \right ) {{\it \_a}}^{2} \right ) {\frac {1}{\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}}}}+{\frac {2\,{6}^{2/3}}{3} \left ( \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}+{\it \_f}\, \left ( {\frac {\sqrt {3}}{2} \left ( {\frac {27\,{\it \_a}\,{\it \_f}-2}{{\it \_a}}}+27\,{\it \_f} \right ) {\frac {1}{\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}}}}-9 \right ) {{\it \_a}}^{2} \right ) {\frac {1}{\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}}}}+12\,{\it \_a}\,\sqrt [3]{6}\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}+4\,{{\it \_a}\,{\it \_f}\,\sqrt [3]{6} \left ( \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}+{\it \_f}\, \left ( 1/2\,{\sqrt {3} \left ( {\frac {27\,{\it \_a}\,{\it \_f}-2}{{\it \_a}}}+27\,{\it \_f} \right ) {\frac {1}{\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}}}}-9 \right ) {{\it \_a}}^{2} \right ) \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{-2/3}}-6\,i\sqrt {3}{\it \_a}+6\,{\it \_a} \right ) \left ( i{6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}\sqrt {3}+{6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}-6\,i\sqrt {3}{\it \_a}\,{\it \_f}+6\,{\it \_a}\,{\it \_f} \right ) ^{-1}}+{\frac {1}{{\it \_a}} \left ( i{6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}\sqrt {3}+{6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}+12\,{\it \_f}\,{\it \_a}\,\sqrt [3]{6}\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}-6\,i\sqrt {3}{\it \_a}\,{\it \_f}+6\,{\it \_a}\,{\it \_f} \right ) \left ( {{\frac {2\,i}{3}}{6}^{{\frac {2}{3}}}\sqrt {3} \left ( \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}+{\it \_f}\, \left ( {\frac {\sqrt {3}}{2} \left ( {\frac {27\,{\it \_a}\,{\it \_f}-2}{{\it \_a}}}+27\,{\it \_f} \right ) {\frac {1}{\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}}}}-9 \right ) {{\it \_a}}^{2} \right ) {\frac {1}{\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}}}}+{\frac {2\,{6}^{2/3}}{3} \left ( \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}+{\it \_f}\, \left ( {\frac {\sqrt {3}}{2} \left ( {\frac {27\,{\it \_a}\,{\it \_f}-2}{{\it \_a}}}+27\,{\it \_f} \right ) {\frac {1}{\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}}}}-9 \right ) {{\it \_a}}^{2} \right ) {\frac {1}{\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}}}}-6\,i\sqrt {3}{\it \_a}+6\,{\it \_a} \right ) \left ( i{6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}\sqrt {3}+{6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}-6\,i\sqrt {3}{\it \_a}\,{\it \_f}+6\,{\it \_a}\,{\it \_f} \right ) ^{-2}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0,\int _{{\it \_b}}^{x}\!-{\frac {1}{{\it \_a}} \left ( i{6}^{{\frac {2}{3}}} \left ( y \left ( x \right ) \left ( \sqrt {3}\sqrt {{\frac {y \left ( x \right ) \left ( 27\,{\it \_a}\,y \left ( x \right ) -2 \right ) }{{\it \_a}}}}-9\,y \left ( x \right ) \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}\sqrt {3}-6\,i\sqrt {3}{\it \_a}\,y \left ( x \right ) -{6}^{{\frac {2}{3}}} \left ( y \left ( x \right ) \left ( \sqrt {3}\sqrt {{\frac {y \left ( x \right ) \left ( 27\,{\it \_a}\,y \left ( x \right ) -2 \right ) }{{\it \_a}}}}-9\,y \left ( x \right ) \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}-12\,y \left ( x \right ) {\it \_a}\,\sqrt [3]{6}\sqrt [3]{y \left ( x \right ) \left ( \sqrt {3}\sqrt {{\frac {y \left ( x \right ) \left ( 27\,{\it \_a}\,y \left ( x \right ) -2 \right ) }{{\it \_a}}}}-9\,y \left ( x \right ) \right ) {{\it \_a}}^{2}}-6\,{\it \_a}\,y \left ( x \right ) \right ) \left ( i{6}^{{\frac {2}{3}}} \left ( y \left ( x \right ) \left ( \sqrt {3}\sqrt {{\frac {y \left ( x \right ) \left ( 27\,{\it \_a}\,y \left ( x \right ) -2 \right ) }{{\it \_a}}}}-9\,y \left ( x \right ) \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}\sqrt {3}-{6}^{{\frac {2}{3}}} \left ( y \left ( x \right ) \left ( \sqrt {3}\sqrt {{\frac {y \left ( x \right ) \left ( 27\,{\it \_a}\,y \left ( x \right ) -2 \right ) }{{\it \_a}}}}-9\,y \left ( x \right ) \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}-6\,i\sqrt {3}{\it \_a}\,y \left ( x \right ) -6\,{\it \_a}\,y \left ( x \right ) \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!12\,{x\sqrt [3]{6}\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,x{\it \_f}-2 \right ) }{x}}}-9\,{\it \_f} \right ) {x}^{2}} \left ( i{6}^{2/3} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,x{\it \_f}-2 \right ) }{x}}}-9\,{\it \_f} \right ) {x}^{2} \right ) ^{2/3}\sqrt {3}-{6}^{2/3} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,x{\it \_f}-2 \right ) }{x}}}-9\,{\it \_f} \right ) {x}^{2} \right ) ^{2/3}-6\,i\sqrt {3}x{\it \_f}-6\,x{\it \_f} \right ) ^{-1}}-\int _{{\it \_b}}^{x}\!-{\frac {1}{{\it \_a}} \left ( {{\frac {2\,i}{3}}{6}^{{\frac {2}{3}}}\sqrt {3} \left ( \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}+{\it \_f}\, \left ( {\frac {\sqrt {3}}{2} \left ( {\frac {27\,{\it \_a}\,{\it \_f}-2}{{\it \_a}}}+27\,{\it \_f} \right ) {\frac {1}{\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}}}}-9 \right ) {{\it \_a}}^{2} \right ) {\frac {1}{\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}}}}-6\,i\sqrt {3}{\it \_a}-{\frac {2\,{6}^{2/3}}{3} \left ( \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}+{\it \_f}\, \left ( {\frac {\sqrt {3}}{2} \left ( {\frac {27\,{\it \_a}\,{\it \_f}-2}{{\it \_a}}}+27\,{\it \_f} \right ) {\frac {1}{\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}}}}-9 \right ) {{\it \_a}}^{2} \right ) {\frac {1}{\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}}}}-12\,{\it \_a}\,\sqrt [3]{6}\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}-4\,{{\it \_a}\,{\it \_f}\,\sqrt [3]{6} \left ( \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}+{\it \_f}\, \left ( 1/2\,{\sqrt {3} \left ( {\frac {27\,{\it \_a}\,{\it \_f}-2}{{\it \_a}}}+27\,{\it \_f} \right ) {\frac {1}{\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}}}}-9 \right ) {{\it \_a}}^{2} \right ) \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{-2/3}}-6\,{\it \_a} \right ) \left ( i{6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}\sqrt {3}-{6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}-6\,i\sqrt {3}{\it \_a}\,{\it \_f}-6\,{\it \_a}\,{\it \_f} \right ) ^{-1}}+{\frac {1}{{\it \_a}} \left ( i{6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}\sqrt {3}-6\,i\sqrt {3}{\it \_a}\,{\it \_f}-{6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}-12\,{\it \_f}\,{\it \_a}\,\sqrt [3]{6}\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}-6\,{\it \_a}\,{\it \_f} \right ) \left ( {{\frac {2\,i}{3}}{6}^{{\frac {2}{3}}}\sqrt {3} \left ( \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}+{\it \_f}\, \left ( {\frac {\sqrt {3}}{2} \left ( {\frac {27\,{\it \_a}\,{\it \_f}-2}{{\it \_a}}}+27\,{\it \_f} \right ) {\frac {1}{\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}}}}-9 \right ) {{\it \_a}}^{2} \right ) {\frac {1}{\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}}}}-{\frac {2\,{6}^{2/3}}{3} \left ( \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}+{\it \_f}\, \left ( {\frac {\sqrt {3}}{2} \left ( {\frac {27\,{\it \_a}\,{\it \_f}-2}{{\it \_a}}}+27\,{\it \_f} \right ) {\frac {1}{\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}}}}-9 \right ) {{\it \_a}}^{2} \right ) {\frac {1}{\sqrt [3]{{\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2}}}}}-6\,i\sqrt {3}{\it \_a}-6\,{\it \_a} \right ) \left ( i{6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}\sqrt {3}-{6}^{{\frac {2}{3}}} \left ( {\it \_f}\, \left ( \sqrt {3}\sqrt {{\frac {{\it \_f}\, \left ( 27\,{\it \_a}\,{\it \_f}-2 \right ) }{{\it \_a}}}}-9\,{\it \_f} \right ) {{\it \_a}}^{2} \right ) ^{{\frac {2}{3}}}-6\,i\sqrt {3}{\it \_a}\,{\it \_f}-6\,{\it \_a}\,{\it \_f} \right ) ^{-2}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \]