ODE No. 435

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

\[ x^2 y'(x)^2-2 x y(x) y'(x)+y(x) (y(x)+1)-x=0 \] Mathematica : cpu = 0.0372186 (sec), leaf count = 61

\[\left \{\left \{y(x)\to \frac {1}{4} \left (c_1^2 x-4 i c_1 \sqrt {x}+4 x-4\right )\right \},\left \{y(x)\to \frac {1}{4} \left (c_1^2 x+4 i c_1 \sqrt {x}+4 x-4\right )\right \}\right \}\] Maple : cpu = 2.39 (sec), leaf count = 22

\[ \left \{ y \left ( x \right ) =x,y \left ( x \right ) =\sqrt {x}{\it \_C1}-{\frac {x{{\it \_C1}}^{2}}{4}}+x-1 \right \} \]