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 = 0.346476 (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 = 0.184 (sec), leaf count = 86

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