ODE
\[ \left (y(x)^2+x y(x)+y(x)+1\right ) y'(x)+y(x)+1=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _rational]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.387667 (sec), leaf count = 21
\[\text {Solve}\left [y(x)+x=c_1 e^{-y(x)} (y(x)+1),y(x)\right ]\]
Maple ✓
cpu = 0.093 (sec), leaf count = 36
\[\left [x -\left (-\frac {y \left (x \right ) {\mathrm e}^{y \left (x \right )}}{1+y \left (x \right )}+\textit {\_C1} \right ) \left ({\mathrm e}^{-y \left (x \right )} y \left (x \right )+{\mathrm e}^{-y \left (x \right )}\right ) = 0\right ]\] Mathematica raw input
DSolve[1 + y[x] + (1 + y[x] + x*y[x] + y[x]^2)*y'[x] == 0,y[x],x]
Mathematica raw output
Solve[x + y[x] == (C[1]*(1 + y[x]))/E^y[x], y[x]]
Maple raw input
dsolve((1+y(x)+x*y(x)+y(x)^2)*diff(y(x),x)+1+y(x) = 0, y(x))
Maple raw output
[x-(-1/(1+y(x))*y(x)*exp(y(x))+_C1)*(exp(-y(x))*y(x)+exp(-y(x))) = 0]