3.557   ODE No. 557

\[ \boxed { x \left ( \sqrt { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1}+{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) -y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.016002 (sec), leaf count = 39 \[ \left \{\left \{y(x)\to -\sqrt {c_1 x-x^2}\right \},\left \{y(x)\to \sqrt {c_1 x-x^2}\right \}\right \} \]

Maple: cpu = 0.093 (sec), leaf count = 78 \[ \left \{ {{\it \_C1}{\frac {1}{\sqrt {{\frac { \left ( \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2} \right ) ^{2}}{{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}}} \left ( -{\frac {{x}^{2}- \left ( y \left ( x \right ) \right ) ^{2}}{2\,xy \left ( x \right ) }}+{\frac {1}{ 2}\sqrt {{\frac {{x}^{4}+2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{4}}{{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}} \right ) ^{-1}}+x=0 \right \} \]