2.468   ODE No. 468

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

\[ -4 a^2 x y'(x)+a^2 y(x)+y(x) y'(x)^2=0 \] Mathematica : cpu = 300.48 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 0.083 (sec), leaf count = 181

\[ \left \{ -{\frac {{\it \_C1}\,x}{ay \left ( x \right ) }{\frac {1}{\sqrt [3]{{\frac {a}{y \left ( x \right ) } \left ( 2\,ax+\sqrt {4\,{a}^{2}{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}} \right ) }}}}{\frac {1}{\sqrt [3]{{\frac {{a}^{2}}{ \left ( y \left ( x \right ) \right ) ^{2}} \left ( 2\,{a}^{2}{x}^{2}+\sqrt {4\,{a}^{2}{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}}ax- \left ( y \left ( x \right ) \right ) ^{2} \right ) }}}}}+x=0,-{\frac {{\it \_C1}\,x}{ay \left ( x \right ) }{\frac {1}{\sqrt [3]{-{\frac {a}{y \left ( x \right ) } \left ( -2\,ax+\sqrt {4\,{a}^{2}{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}} \right ) }}}}{\frac {1}{\sqrt [3]{-4\,{\frac {{a}^{2} \left ( -2\,{a}^{2}{x}^{2}+\sqrt {4\,{a}^{2}{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}}ax+ \left ( y \left ( x \right ) \right ) ^{2} \right ) }{ \left ( y \left ( x \right ) \right ) ^{2}}}}}}}+x=0 \right \} \]