2.543   ODE No. 543

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

\[ x \left (x^2+1\right ) y'(x)-x^2 y(x)+y(x)^3 \left (-y'(x)^2\right )+x y(x)^2 y'(x)^3=0 \] Mathematica : cpu = 300.006 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 12.393 (sec), leaf count = 277

\[ \left \{ y \left ( x \right ) =-{\frac {i}{2}}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2-2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}},y \left ( x \right ) =-{\frac {i}{2}}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2+2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}},y \left ( x \right ) ={\frac {i}{2}}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2-2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}},y \left ( x \right ) ={\frac {i}{2}}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2+2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}},y \left ( x \right ) =-{\frac {1}{2}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2-2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}}},y \left ( x \right ) ={\frac {1}{2}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2-2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}}},y \left ( x \right ) =-{\frac {1}{2}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2+2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}}},y \left ( x \right ) ={\frac {1}{2}\sqrt [4]{-16\,{x}^{4}+40\,{x}^{2}+2+2\,\sqrt {- \left ( 8\,{x}^{2}-1 \right ) ^{3}}}} \right \} \]