2.509   ODE No. 509

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

\[ 9 \left (x^2-1\right ) y(x)^4 y'(x)^2-4 x^2-6 x y(x)^5 y'(x)=0 \] Mathematica : cpu = 3651.62 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 1.463 (sec), leaf count = 245

\[ \left \{ y \left ( x \right ) =\sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) = \left ( -{\frac {1}{2}}-{\frac {i}{2}}\sqrt {3} \right ) \sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) = \left ( -{\frac {1}{2}}+{\frac {i}{2}}\sqrt {3} \right ) \sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) = \left ( {\frac {1}{2}}-{\frac {i}{2}}\sqrt {3} \right ) \sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) = \left ( {\frac {1}{2}}+{\frac {i}{2}}\sqrt {3} \right ) \sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) =-\sqrt [6]{-4\,{x}^{2}+4},y \left ( x \right ) ={\frac {1}{2\,{\it \_C1}}\sqrt [3]{ \left ( -16\,{{\it \_C1}}^{2}+4\,{x}^{2}-4 \right ) {{\it \_C1}}^{2}}},y \left ( x \right ) =-{\frac {1}{4\,{\it \_C1}}\sqrt [3]{ \left ( -16\,{{\it \_C1}}^{2}+4\,{x}^{2}-4 \right ) {{\it \_C1}}^{2}}}-{\frac {{\frac {i}{4}}\sqrt {3}}{{\it \_C1}}\sqrt [3]{ \left ( -16\,{{\it \_C1}}^{2}+4\,{x}^{2}-4 \right ) {{\it \_C1}}^{2}}},y \left ( x \right ) =-{\frac {1}{4\,{\it \_C1}}\sqrt [3]{ \left ( -16\,{{\it \_C1}}^{2}+4\,{x}^{2}-4 \right ) {{\it \_C1}}^{2}}}+{\frac {{\frac {i}{4}}\sqrt {3}}{{\it \_C1}}\sqrt [3]{ \left ( -16\,{{\it \_C1}}^{2}+4\,{x}^{2}-4 \right ) {{\it \_C1}}^{2}}} \right \} \]