2.116   ODE No. 116

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

\[ -x \sqrt {\left (y(x)^2-4 x^2\right ) \left (y(x)^2-x^2\right )}+x y'(x)-y(x)=0 \] Mathematica : cpu = 3.99901 (sec), leaf count = 142

\[\text {Solve}\left [\frac {2 \sqrt {\frac {y(x)+x}{2 x-y(x)}} \sqrt {\frac {y(x)+2 x}{2 x-y(x)}} \left (\frac {y(x)}{x}-2\right )^{3/2} \sqrt {\frac {1}{\frac {y(x)}{x}-2}+1} F\left (\left .\sin ^{-1}\left (\sqrt {\frac {x+y(x)}{4 x-2 y(x)}}\right )\right |-8\right )}{\sqrt {\frac {y(x)+x}{x}} \sqrt {\frac {y(x)}{x}-1} \sqrt {\frac {y(x)}{x}+2}}=c_1+\frac {x^2}{2},y(x)\right ]\]

Maple : cpu = 0.229 (sec), leaf count = 86

\[ \left \{ \int _{{\it \_b}}^{x}\!{1 \left ( {\it \_a}\,\sqrt {4\,{{\it \_a}}^{4}-5\,{{\it \_a}}^{2} \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{4}}+y \left ( x \right ) \right ) {\frac {1}{\sqrt {4\,{{\it \_a}}^{4}-5\,{{\it \_a}}^{2} \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{4}}}}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!-{{\it \_b}{\frac {1}{\sqrt {4\,{{\it \_b}}^{4}-5\,{{\it \_b}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}}}}}{d{\it \_f}}+{\it \_C1}=0 \right \} \]