2.18   ODE No. 18

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

\[ y'(x)-y(x)^2-x y(x)-x+1=0 \] Mathematica : cpu = 0.0406162 (sec), leaf count = 50

\[\left \{\left \{y(x)\to \frac {e^{\frac {x^2}{2}-2 x}}{c_1-\frac {\sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {x-2}{\sqrt {2}}\right )}{e^2}}-1\right \}\right \}\]

Maple : cpu = 0.078 (sec), leaf count = 47

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