2.62   ODE No. 62

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

\[ y'(x)-\frac {y(x)-x^2 \sqrt {x^2-y(x)^2}}{x y(x) \sqrt {x^2-y(x)^2}+x}=0 \] Mathematica : cpu = 3.75953 (sec), leaf count = 40

\[\text {Solve}\left [\tan ^{-1}\left (\frac {y(x)}{\sqrt {x^2-y(x)^2}}\right )+\frac {x^2}{2}+\frac {y(x)^2}{2}=c_1,y(x)\right ]\]

Maple : cpu = 0.406 (sec), leaf count = 34

\[ \left \{ {\frac { \left ( y \left ( x \right ) \right ) ^{2}}{2}}+\arctan \left ( {y \left ( x \right ) {\frac {1}{\sqrt {{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}}}}} \right ) +{\frac {{x}^{2}}{2}}-{\it \_C1}=0 \right \} \]