ODE
\[ y'(x)-x+1=y(x) (y(x)+x) \] ODE Classification
[_Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.0236493 (sec), leaf count = 49
\[\left \{\left \{y(x)\to \frac {2 e^{\frac {1}{2} (x-2)^2}}{2 e^2 c_1-\sqrt {2 \pi } \text {erfi}\left (\frac {x-2}{\sqrt {2}}\right )}-1\right \}\right \}\]
Maple ✓
cpu = 0.092 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) =-1+{\frac {1}{{\it \_C1}+{\frac {i}{2}}\sqrt {\pi }{{\rm e}^{-2}}\sqrt {2}{\it Erf} \left ( {\frac {i}{2}}\sqrt {2} \left ( x-2 \right ) \right ) }{{\rm e}^{{\frac {x \left ( x-4 \right ) }{2}}}}} \right \} \] Mathematica raw input
DSolve[1 - x + y'[x] == y[x]*(x + y[x]),y[x],x]
Mathematica raw output
{{y[x] -> -1 + (2*E^((-2 + x)^2/2))/(2*E^2*C[1] - Sqrt[2*Pi]*Erfi[(-2 + x)/Sqrt[2]])}}
Maple raw input
dsolve(diff(y(x),x)+1-x = (x+y(x))*y(x), y(x),'implicit')
Maple raw output
y(x) = -1+exp(1/2*x*(x-4))/(_C1+1/2*I*Pi^(1/2)*exp(-2)*2^(1/2)*erf(1/2*I*2^(1/2)*(x-2)))