#### 2.544   ODE No. 544

$x^7 y(x)^2 y'(x)^3-\left (3 x^6 y(x)^3-1\right ) y'(x)^2+3 x^5 y(x)^4 y'(x)-x^4 y(x)^5=0$ Mathematica : cpu = 0.0727555 (sec), leaf count = 22

$\left \{\left \{y(x)\to \sqrt [3]{c_1 x^3+c_1{}^{2/3}}\right \}\right \}$ Maple : cpu = 0.697 (sec), leaf count = 4201

$\left \{ \int _{{\it \_b}}^{x}\!{\frac {1}{{\it \_a}} \left ( \left ( -1-i\sqrt {3} \right ) \left ( -108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8 \right ) ^{{\frac {2}{3}}}+ \left ( 12\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4 \right ) \sqrt [3]{-108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8}-24\, \left ( {{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-1/6 \right ) \left ( i\sqrt {3}-1 \right ) \right ) \left ( 24\,i\sqrt {3}{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-36\,\sqrt [3]{-108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8}{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-24\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}+i \left ( -108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8 \right ) ^{{\frac {2}{3}}}\sqrt {3}-4\,i\sqrt {3}+ \left ( -108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8 \right ) ^{{\frac {2}{3}}}+4\,\sqrt [3]{-108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8}+4 \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!-12\,{{x}^{6}{{\it \_f}}^{2}\sqrt [3]{-108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8} \left ( 24\,i\sqrt {3}{x}^{6}{{\it \_f}}^{3}-36\,\sqrt [3]{-108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8}{x}^{6}{{\it \_f}}^{3}-24\,{x}^{6}{{\it \_f}}^{3}+i \left ( -108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}\sqrt {3}-4\,i\sqrt {3}+ \left ( -108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}+4\,\sqrt [3]{-108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8}+4 \right ) ^{-1}}-\int _{{\it \_b}}^{x}\!-62208\,{{{\it \_a}}^{5}{{\it \_f}}^{2} \left ( {{{\it \_a}}^{6}{{\it \_f}}^{3} \left ( {\sqrt {3}{\it \_f}\,{{\it \_a}}^{3} \left ( {{\it \_a}}^{6}{{\it \_f}}^{3}+{\frac {2}{27}} \right ) {\frac {1}{\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}}}}-2\,{{\it \_a}}^{6}{{\it \_f}}^{3}+{\frac {5\,\sqrt {3}{{\it \_f}}^{2}{{\it \_a}}^{3}}{27}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}}+2/3 \right ) \left ( \left ( i/24\sqrt {3}+1/24 \right ) \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}+ \left ( {{\it \_a}}^{6}{{\it \_f}}^{3}-1/6 \right ) \left ( i\sqrt {3}-1 \right ) \right ) \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{-2/3}}-1/12\,\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8} \left ( \left ( -{\frac {i}{72}}\sqrt {3}-{\frac {1}{72}} \right ) \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}+{{{\it \_a}}^{6} \left ( i\sqrt {3}+1 \right ) {{\it \_f}}^{3} \left ( {\sqrt {3}{\it \_f}\,{{\it \_a}}^{3} \left ( {{\it \_a}}^{6}{{\it \_f}}^{3}+{\frac {2}{27}} \right ) {\frac {1}{\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}}}}-2\,{{\it \_a}}^{6}{{\it \_f}}^{3}+{\frac {5\,\sqrt {3}{{\it \_f}}^{2}{{\it \_a}}^{3}}{27}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}}+2/3 \right ) {\frac {1}{\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8}}}}+i/18\sqrt {3}-1/18\,\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8}-1/18 \right ) \right ) \left ( 24\,i\sqrt {3}{{\it \_a}}^{6}{{\it \_f}}^{3}-36\,\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8}{{\it \_a}}^{6}{{\it \_f}}^{3}-24\,{{\it \_a}}^{6}{{\it \_f}}^{3}+i \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}\sqrt {3}-4\,i\sqrt {3}+ \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}+4\,\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8}+4 \right ) ^{-2}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0,\int _{{\it \_b}}^{x}\!{\frac {1}{{\it \_a}} \left ( \left ( -i\sqrt {3}+1 \right ) \left ( -108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8 \right ) ^{{\frac {2}{3}}}+ \left ( -12\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}+4 \right ) \sqrt [3]{-108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8}-24\, \left ( {{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-1/6 \right ) \left ( i\sqrt {3}+1 \right ) \right ) \left ( 24\,i\sqrt {3}{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}+36\,\sqrt [3]{-108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8}{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}+24\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}+i \left ( -108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8 \right ) ^{{\frac {2}{3}}}\sqrt {3}-4\,i\sqrt {3}- \left ( -108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8 \right ) ^{{\frac {2}{3}}}-4\,\sqrt [3]{-108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8}-4 \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!12\,{{x}^{6}{{\it \_f}}^{2}\sqrt [3]{-108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8} \left ( 24\,i\sqrt {3}{x}^{6}{{\it \_f}}^{3}+36\,\sqrt [3]{-108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8}{x}^{6}{{\it \_f}}^{3}+24\,{x}^{6}{{\it \_f}}^{3}+i \left ( -108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}\sqrt {3}-4\,i\sqrt {3}- \left ( -108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}-4\,\sqrt [3]{-108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8}-4 \right ) ^{-1}}-\int _{{\it \_b}}^{x}\!62208\,{{{\it \_a}}^{5}{{\it \_f}}^{2} \left ( {{{\it \_a}}^{6}{{\it \_f}}^{3} \left ( \left ( i/24\sqrt {3}-1/24 \right ) \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}+ \left ( {{\it \_a}}^{6}{{\it \_f}}^{3}-1/6 \right ) \left ( i\sqrt {3}+1 \right ) \right ) \left ( {\sqrt {3}{\it \_f}\,{{\it \_a}}^{3} \left ( {{\it \_a}}^{6}{{\it \_f}}^{3}+{\frac {2}{27}} \right ) {\frac {1}{\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}}}}-2\,{{\it \_a}}^{6}{{\it \_f}}^{3}+{\frac {5\,\sqrt {3}{{\it \_f}}^{2}{{\it \_a}}^{3}}{27}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}}+2/3 \right ) \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{-2/3}}-1/12\, \left ( \left ( -{\frac {i}{72}}\sqrt {3}+{\frac {1}{72}} \right ) \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}+{{{\it \_a}}^{6} \left ( i\sqrt {3}-1 \right ) {{\it \_f}}^{3} \left ( {\sqrt {3}{\it \_f}\,{{\it \_a}}^{3} \left ( {{\it \_a}}^{6}{{\it \_f}}^{3}+{\frac {2}{27}} \right ) {\frac {1}{\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}}}}-2\,{{\it \_a}}^{6}{{\it \_f}}^{3}+{\frac {5\,\sqrt {3}{{\it \_f}}^{2}{{\it \_a}}^{3}}{27}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}}+2/3 \right ) {\frac {1}{\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8}}}}+i/18\sqrt {3}+1/18\,\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8}+1/18 \right ) \sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8} \right ) \left ( 24\,i\sqrt {3}{{\it \_a}}^{6}{{\it \_f}}^{3}+36\,\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8}{{\it \_a}}^{6}{{\it \_f}}^{3}+24\,{{\it \_a}}^{6}{{\it \_f}}^{3}+i \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}\sqrt {3}-4\,i\sqrt {3}- \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}-4\,\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8}-4 \right ) ^{-2}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0,\int _{{\it \_b}}^{x}\!{\frac {1}{{\it \_a}} \left ( -6\,\sqrt [3]{-108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8}{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}+24\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}+2\,\sqrt [3]{-108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8}- \left ( -108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8 \right ) ^{{\frac {2}{3}}}-4 \right ) \left ( 18\,\sqrt [3]{-108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8}{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-24\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}+ \left ( -108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8 \right ) ^{{\frac {2}{3}}}-2\,\sqrt [3]{-108\, \left ( y \left ( x \right ) \right ) ^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-4}{y \left ( x \right ) }}} \left ( y \left ( x \right ) \right ) ^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6} \left ( y \left ( x \right ) \right ) ^{3}-8}+4 \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!6\,{{x}^{6}{{\it \_f}}^{2}\sqrt [3]{-108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8} \left ( 18\,\sqrt [3]{-108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8}{x}^{6}{{\it \_f}}^{3}-24\,{x}^{6}{{\it \_f}}^{3}+ \left ( -108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}-2\,\sqrt [3]{-108\,{{\it \_f}}^{6}{x}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{x}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{x}^{9}+72\,{x}^{6}{{\it \_f}}^{3}-8}+4 \right ) ^{-1}}-\int _{{\it \_b}}^{x}\!-31104\,{{{\it \_a}}^{5}{{\it \_f}}^{2} \left ( {{{\it \_a}}^{6}{{\it \_f}}^{3} \left ( {\sqrt {3}{\it \_f}\,{{\it \_a}}^{3} \left ( {{\it \_a}}^{6}{{\it \_f}}^{3}+{\frac {2}{27}} \right ) {\frac {1}{\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}}}}-2\,{{\it \_a}}^{6}{{\it \_f}}^{3}+{\frac {5\,\sqrt {3}{{\it \_f}}^{2}{{\it \_a}}^{3}}{27}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}}+2/3 \right ) \left ( {{\it \_a}}^{6}{{\it \_f}}^{3}-1/24\, \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}-1/6 \right ) \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{-2/3}}+1/12\,\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8} \left ( -{\frac {1}{72} \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}}+{{{\it \_a}}^{6}{{\it \_f}}^{3} \left ( {\sqrt {3}{\it \_f}\,{{\it \_a}}^{3} \left ( {{\it \_a}}^{6}{{\it \_f}}^{3}+{\frac {2}{27}} \right ) {\frac {1}{\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}}}}-2\,{{\it \_a}}^{6}{{\it \_f}}^{3}+{\frac {5\,\sqrt {3}{{\it \_f}}^{2}{{\it \_a}}^{3}}{27}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}}+2/3 \right ) {\frac {1}{\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8}}}}+1/36\,\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8}-1/18 \right ) \right ) \left ( 18\,\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8}{{\it \_a}}^{6}{{\it \_f}}^{3}-24\,{{\it \_a}}^{6}{{\it \_f}}^{3}+ \left ( -108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8 \right ) ^{2/3}-2\,\sqrt [3]{-108\,{{\it \_f}}^{6}{{\it \_a}}^{12}+12\,\sqrt {3}\sqrt {{\frac {27\,{{\it \_a}}^{6}{{\it \_f}}^{3}-4}{{\it \_f}}}}{{\it \_f}}^{5}{{\it \_a}}^{9}+72\,{{\it \_a}}^{6}{{\it \_f}}^{3}-8}+4 \right ) ^{-2}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0,y \left ( x \right ) ={\frac {{2}^{{\frac {2}{3}}}}{3\,{x}^{2}}},y \left ( x \right ) ={\frac {{2}^{{\frac {2}{3}}} \left ( i\sqrt {3}-1 \right ) }{6\,{x}^{2}}},y \left ( x \right ) =-{\frac {{2}^{{\frac {2}{3}}} \left ( i\sqrt {3}+1 \right ) }{6\,{x}^{2}}} \right \}$