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 = 0.0330663 (sec), leaf count = 26

\[\left \{\left \{y(x)\to -x \sinh \left (x-c_1\right )\right \},\left \{y(x)\to x \sinh \left (c_1+x\right )\right \}\right \}\]

Maple : cpu = 1.867 (sec), leaf count = 59

\[ \left \{ y \left ( x \right ) =-ix,y \left ( x \right ) =ix,y \left ( x \right ) =-{\frac {{\it \_C1}\,x}{2\,{{\rm e}^{x}}} \left ( {\frac { \left ( {{\rm e}^{x}} \right ) ^{2}}{{{\it \_C1}}^{2}}}-1 \right ) },y \left ( x \right ) ={\frac {x \left ( \left ( {{\rm e}^{x}} \right ) ^{2}{{\it \_C1}}^{2}-1 \right ) }{2\,{\it \_C1}\,{{\rm e}^{x}}}} \right \} \]