ODE
\[ y'(x)-x+1=y(x) (y(x)+x) \] ODE Classification
[_Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.259409 (sec), leaf count = 49
\[\left \{\left \{y(x)\to -1+\frac {2 e^{\frac {1}{2} (x-2)^2}}{-\sqrt {2 \pi } \text {erfi}\left (\frac {x-2}{\sqrt {2}}\right )+2 e^2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.09 (sec), leaf count = 47
\[\left [y \left (x \right ) = -1+\frac {{\mathrm e}^{\frac {1}{2} x^{2}-2 x}}{\textit {\_C1} +\frac {i \sqrt {\pi }\, {\mathrm e}^{-2} \sqrt {2}\, \erf \left (\frac {i \sqrt {2}\, x}{2}-i \sqrt {2}\right )}{2}}\right ]\] 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))
Maple raw output
[y(x) = -1+exp(1/2*x^2-2*x)/(_C1+1/2*I*Pi^(1/2)*exp(-2)*2^(1/2)*erf(1/2*I*2^(1/2)*x-I*2^(1/2)))]