3.62   ODE No. 62

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -{\frac {y \left ( x \right ) -{x}^{2}\sqrt {{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}}}{xy \left ( x \right ) \sqrt {{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}}+x}}=0} \]

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

Mathematica: cpu = 3.807984 (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 = 0.297 (sec), leaf count = 34 \[ \left \{ {\frac { \left ( y \left ( x \right ) \right ) ^{2}}{2}}+\arctan \left ( {y \left ( x \right ) {\frac {1}{\sqrt {{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}}}}} \right ) +{\frac {{x}^{2}}{2}}-{ \it \_C1}=0 \right \} \]

Sage: cpu = 0 (sec), leaf count = 0 \[ \text {Maxima was unable to solve this ODE} \]