2.530   ODE No. 530

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ y'(x)^3-y(x) y'(x)^2+y(x)^2=0 \] Mathematica : cpu = 300.014 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 0.666 (sec), leaf count = 432

\[ \left \{ x-\int ^{y \left ( x \right ) }\!6\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}}{4\,{{\it \_a}}^{2}+2\,{\it \_a}\,\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}+ \left ( -108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}} \right ) ^{2/3}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-24\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}}{ \left ( i\sqrt {3}-1 \right ) \left ( i\sqrt {3}\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}-\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}-4\,{\it \_a} \right ) \left ( 2\,{\it \_a}-\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}} \right ) }}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!24\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}}{ \left ( i\sqrt {3}+1 \right ) \left ( i\sqrt {3}\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}+4\,{\it \_a}+\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}} \right ) \left ( -2\,{\it \_a}+\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}} \right ) }}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =0 \right \} \]