2.436   ODE No. 436

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

\[ -x^4+x^2 y'(x)^2+\left (1-x^2\right ) y(x)^2-2 x y(x) y'(x)=0 \] Mathematica : cpu = 0.0711217 (sec), leaf count = 26

\[\{\{y(x)\to -x \sinh (x-c_1)\},\{y(x)\to x \sinh (x+c_1)\}\}\] Maple : cpu = 2.895 (sec), leaf count = 61

\[\left \{y \left (x \right ) = i x, y \left (x \right ) = -i x, y \left (x \right ) = -\frac {\left (-c_{1}^{2}+{\mathrm e}^{2 x}\right ) x \,{\mathrm e}^{-x}}{2 c_{1}}, y \left (x \right ) = \frac {\left (c_{1}^{2} {\mathrm e}^{2 x}-1\right ) x \,{\mathrm e}^{-x}}{2 c_{1}}\right \}\]