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 = 0.0772691 (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 = 0.047 (sec), leaf count = 52

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