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 = 0.0952307 (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 = 0.049 (sec), leaf count = 44

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