2.524   ODE No. 524

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

\[ y'(x)^3-2 y(x) y'(x)+y(x)^2=0 \] Mathematica : cpu = 640.562 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 0.218 (sec), leaf count = 270

\[ \left \{ x-\int ^{y \left ( x \right ) }\!{{12}^{{\frac {2}{3}}}\sqrt [3]{-9\,{{\it \_a}}^{2}+\sqrt {3}\sqrt {27\,{{\it \_a}}^{4}-32\,{{\it \_a}}^{3}}} \left ( 4\,\sqrt [3]{12}{\it \_a}+2\, \left ( -9\,{{\it \_a}}^{2}+\sqrt {3}\sqrt {27\,{{\it \_a}}^{4}-32\,{{\it \_a}}^{3}} \right ) ^{2/3} \right ) ^{-1}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!{\frac {{12}^{{\frac {2}{3}}}}{1+i\sqrt {3}}\sqrt [3]{-9\,{{\it \_a}}^{2}+\sqrt {3}\sqrt {27\,{{\it \_a}}^{4}-32\,{{\it \_a}}^{3}}} \left ( - \left ( -9\,{{\it \_a}}^{2}+\sqrt {3}\sqrt {27\,{{\it \_a}}^{4}-32\,{{\it \_a}}^{3}} \right ) ^{{\frac {2}{3}}}+\sqrt [3]{12} \left ( 1+i\sqrt {3} \right ) {\it \_a} \right ) ^{-1}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!{\frac {{12}^{{\frac {2}{3}}}}{i\sqrt {3}-1}\sqrt [3]{-9\,{{\it \_a}}^{2}+\sqrt {3}\sqrt {27\,{{\it \_a}}^{4}-32\,{{\it \_a}}^{3}}} \left ( \left ( -9\,{{\it \_a}}^{2}+\sqrt {3}\sqrt {27\,{{\it \_a}}^{4}-32\,{{\it \_a}}^{3}} \right ) ^{{\frac {2}{3}}}+\sqrt [3]{12}{\it \_a}\, \left ( i\sqrt {3}-1 \right ) \right ) ^{-1}}{d{\it \_a}}-{\it \_C1}=0 \right \} \]