ODE
\[ y'(x)=-\left ((1-x) y(x)^2\right )+(1-2 x) y(x)+x \] ODE Classification
[_Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.264645 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {x+c_1 e^x+1}{x+c_1 e^x}\right \}\right \}\]
Maple ✓
cpu = 0.08 (sec), leaf count = 23
\[\left [y \left (x \right ) = 1-\frac {2 \,{\mathrm e}^{-x}}{\textit {\_C1} -2 x \,{\mathrm e}^{-x}}\right ]\] Mathematica raw input
DSolve[y'[x] == x + (1 - 2*x)*y[x] - (1 - x)*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (1 + x + E^x*C[1])/(x + E^x*C[1])}}
Maple raw input
dsolve(diff(y(x),x) = x+(1-2*x)*y(x)-(1-x)*y(x)^2, y(x))
Maple raw output
[y(x) = 1-2*exp(-x)/(_C1-2*x*exp(-x))]