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 = 0.0745803 (sec), leaf count = 59

\[\left \{\left \{y(x)\to \frac {1}{2} \left (-2 e^{-c_1} x^2+2 x-e^{c_1}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (-e^{c_1} x^2+2 x-2 e^{-c_1}\right )\right \}\right \}\] Maple : cpu = 0.06 (sec), leaf count = 44

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