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 = 0 (sec), leaf count = 0 , crash

Kernel Crash

Maple : cpu = 0.174 (sec), leaf count = 421

\[ \left \{ x-\int ^{y \left ( x \right ) }\!6\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }}}{4\,{{\it \_a}}^{2}+2\,{\it \_a}\,\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }}+ \left ( -108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) } \right ) ^{2/3}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!24\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }}}{ \left ( i\sqrt {3}-1 \right ) \left ( 2\,{\it \_a}-\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }} \right ) \left ( -i\sqrt {3}\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }}+4\,{\it \_a}+\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }} \right ) }}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-24\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }}}{ \left ( i\sqrt {3}+1 \right ) \left ( 2\,{\it \_a}-\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }} \right ) \left ( i\sqrt {3}\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }}+4\,{\it \_a}+\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-3\,{{\it \_a}}^{4} \left ( 4\,{\it \_a}-27 \right ) }} \right ) }}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =0 \right \} \]