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 = 0.0345087 (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 = 18.651 (sec), leaf count = 61

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