8.169   ODE No. 1759

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

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

Mathematica: cpu = 0.036505 (sec), leaf count = 18 \[ \left \{\left \{y(x)\to c_2 \sqrt {c_1+x^2}\right \}\right \} \]

Maple: cpu = 1.498 (sec), leaf count = 31 \[ \left \{ y \left ( x \right ) =\sqrt {{\it \_C1}\,{x}^{2}+2\,{\it \_C2}} ,y \left ( x \right ) =-\sqrt {{\it \_C1}\,{x}^{2}+2\,{\it \_C2}} \right \} \]