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 = 0.631941 (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 = 0.23 (sec), leaf count = 86

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