3.423   ODE No. 423

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

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

Mathematica: cpu = 0.078510 (sec), leaf count = 59 \[ \left \{\left \{y(x)\to \frac {1}{2} \left (-2 e^{-c_1} x^2-e^{c_1}+2 x\right )\right \},\left \{y(x)\to \frac {1}{2} \left (-e^{c_1} x^2-2 e^{-c_1}+2 x\right )\right \}\right \} \]

Maple: cpu = 0.515 (sec), leaf count = 52 \[ \left \{ y \left ( x \right ) = \left ( 1-\sqrt {2} \right ) x,y \left ( x \right ) = \left ( 1+\sqrt {2} \right ) x,y \left ( x \right ) =-{x \left ( {\frac { \left ( x+{\it \_C1} \right ) ^{2}}{{{\it \_C1}}^{2}}}+ 1 \right ) \left ( -2\,{\frac {x+{\it \_C1}}{{\it \_C1}}}+2 \right ) ^{- 1}} \right \} \]