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

timed out

Maple : cpu = 0.056 (sec), leaf count = 295

\[ \left \{ x-\int ^{y \left ( x \right ) }\!6\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {{{\it \_a}}^{3} \left ( 27\,{\it \_a}-32 \right ) }}}{ \left ( -108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {{{\it \_a}}^{3} \left ( 27\,{\it \_a}-32 \right ) } \right ) ^{2/3}+24\,{\it \_a}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!24\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {{{\it \_a}}^{3} \left ( 27\,{\it \_a}-32 \right ) }}}{ \left ( i\sqrt {3}-1 \right ) \left ( i \left ( -108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {{{\it \_a}}^{3} \left ( 27\,{\it \_a}-32 \right ) } \right ) ^{2/3}\sqrt {3}- \left ( -108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {{{\it \_a}}^{3} \left ( 27\,{\it \_a}-32 \right ) } \right ) ^{2/3}+48\,{\it \_a} \right ) }}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-24\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {{{\it \_a}}^{3} \left ( 27\,{\it \_a}-32 \right ) }}}{ \left ( i\sqrt {3}+1 \right ) \left ( -i \left ( -108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {{{\it \_a}}^{3} \left ( 27\,{\it \_a}-32 \right ) } \right ) ^{2/3}\sqrt {3}- \left ( -108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {{{\it \_a}}^{3} \left ( 27\,{\it \_a}-32 \right ) } \right ) ^{2/3}+48\,{\it \_a} \right ) }}{d{\it \_a}}-{\it \_C1}=0 \right \} \]