#### 2.116   ODE No. 116

$-x \sqrt {\left (y(x)^2-4 x^2\right ) \left (y(x)^2-x^2\right )}+x y'(x)-y(x)=0$ Mathematica : cpu = 0.350461 (sec), leaf count = 121

$\text {Solve}\left [\frac {\sqrt {\frac {\frac {y(x)}{x}+2}{\frac {y(x)}{x}-1}} \sqrt {\frac {\frac {y(x)}{x}+1}{\frac {2 y(x)}{x}+4}} F\left (\sin ^{-1}\left (\sqrt {\frac {2}{3}} \sqrt {\frac {\frac {y(x)}{x}-2}{\frac {y(x)}{x}-1}}\right )|\frac {9}{8}\right )}{\sqrt {\frac {\frac {y(x)}{x}+1}{\frac {y(x)}{x}-1}}}=c_1+\frac {x^2}{2},y(x)\right ]$ Maple : cpu = 0.174 (sec), leaf count = 86

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