#### 2.562   ODE No. 562

$a \sqrt [3]{y'(x)^3+1}+b x y'(x)-y(x)=0$ Mathematica : cpu = 300.007 (sec), leaf count = 0 , timed out

\$Aborted

Maple : cpu = 0.463 (sec), leaf count = 3306

$\left \{ \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 ) \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}}}+x=0, \left ( -\int ^{4\,{\frac {1/4\,a \left ( -1+i\sqrt {3} \right ) \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 ) ^{2/3}+ \left ( bx\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}}}+{a}^{2}y \left ( x \right ) \left ( 1+i\sqrt {3} \right ) \right ) y \left ( x \right ) xb}{\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}}} \left ( 4\,{b}^{3}{x}^{3}+4\,{a}^{3} \right ) }}}\!-{\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 ) \left ( 4\,{\frac {1/4\,a \left ( -1+i\sqrt {3} \right ) \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 ) ^{2/3}+ \left ( bx\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}}}+{a}^{2}y \left ( x \right ) \left ( 1+i\sqrt {3} \right ) \right ) y \left ( x \right ) xb}{\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}}} \left ( 4\,{b}^{3}{x}^{3}+4\,{a}^{3} \right ) }} \right ) ^{-{\frac {b}{b-1}}}+x=0, \left ( -\int ^{-4\,{\frac {1/4\,a \left ( 1+i\sqrt {3} \right ) \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 ) ^{2/3}+y \left ( x \right ) x \left ( -bx\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}}}+{a}^{2}y \left ( x \right ) \left ( -1+i\sqrt {3} \right ) \right ) b}{\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}}} \left ( 4\,{b}^{3}{x}^{3}+4\,{a}^{3} \right ) }}}\!-{\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 ) \left ( -4\,{\frac {1/4\,a \left ( 1+i\sqrt {3} \right ) \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 ) ^{2/3}+y \left ( x \right ) x \left ( -bx\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}}}+{a}^{2}y \left ( x \right ) \left ( -1+i\sqrt {3} \right ) \right ) b}{\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}}} \left ( 4\,{b}^{3}{x}^{3}+4\,{a}^{3} \right ) }} \right ) ^{-{\frac {b}{b-1}}}+x=0 \right \}$