3.18   ODE No. 18

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}-xy \left ( x \right ) -x+1=0} \]

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

Mathematica: cpu = 0.020503 (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 = 0.062 (sec), leaf count = 47 \[ \left \{ y \left ( x \right ) =-1+{\frac {1}{{\it \_C1}+{\frac {i}{2}} \sqrt {\pi }{{\rm e}^{-2}}\sqrt {2}{\it Erf} \left ( {\frac {i}{2}} \sqrt {2}x-i\sqrt {2} \right ) }{{\rm e}^{{\frac {{x}^{2}}{2}}-2\,x}}} \right \} \]

Sage: cpu = 0.076 (sec), leaf count = 0 \[ \left [\left [y\left (x\right ) = -\frac {\sqrt {\pi } c e^{2} + \sqrt {\pi } \text {erf}\left (\frac {1}{2} \, \sqrt {2} {\left (i \, x - 2 i\right )}\right ) + i \, \sqrt {2} e^{\left (\frac {1}{2} \, {\left (x - 2\right )}^{2}\right )}}{\sqrt {\pi } c e^{2} + \sqrt {\pi } \text {erf}\left (\frac {1}{2} \, \sqrt {2} {\left (i \, x - 2 i\right )}\right )}\right ], \text {\texttt {riccati}}\right ] \]