2.423   ODE No. 423

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

\[ x y'(x)^2-2 y(x) y'(x)+2 y(x)+x=0 \] Mathematica : cpu = 0.0767615 (sec), leaf count = 51

\[\left \{\left \{y(x)\to -e^{-c_1} x^2-\frac {e^{c_1}}{2}+x\right \},\left \{y(x)\to -\frac {1}{2} e^{c_1} x^2-e^{-c_1}+x\right \}\right \}\]

Maple : cpu = 0.042 (sec), leaf count = 44

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