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 = 315.379 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 0.165 (sec), leaf count = 370

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