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 = 0.547666 (sec), leaf count = 121


\[\text {Solve}\left [\frac {\sqrt {\frac {\frac {y(x)}{x}+2}{\frac {y(x)}{x}-1}} \sqrt {\frac {\frac {y(x)}{x}+1}{\frac {2 y(x)}{x}+4}} F\left (\sin ^{-1}\left (\sqrt {\frac {2}{3}} \sqrt {\frac {\frac {y(x)}{x}-2}{\frac {y(x)}{x}-1}}\right )|\frac {9}{8}\right )}{\sqrt {\frac {\frac {y(x)}{x}+1}{\frac {y(x)}{x}-1}}}=\frac {x^2}{2}+c_1,y(x)\right ]\] Maple : cpu = 0.229 (sec), leaf count = 86


\[\int _{\textit {\_b}}^{x}\frac {\textit {\_a} \sqrt {4 \textit {\_a}^{4}-5 \textit {\_a}^{2} y \relax (x )^{2}+y \relax (x )^{4}}+y \relax (x )}{\sqrt {4 \textit {\_a}^{4}-5 \textit {\_a}^{2} y \relax (x )^{2}+y \relax (x )^{4}}}d \textit {\_a} +\int _{}^{y \relax (x )}-\frac {\textit {\_b}}{\sqrt {4 \textit {\_b}^{4}-5 \textit {\_b}^{2} \textit {\_f}^{2}+\textit {\_f}^{4}}}d \textit {\_f} +c_{1} = 0\]