4.13.16 \(\left (y(x)^2+x y(x)+y(x)+1\right ) y'(x)+y(x)+1=0\)

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 = 0.0654704 (sec), leaf count = 21

\[\text {Solve}\left [y(x)+x=c_1 e^{-y(x)} (y(x)+1),y(x)\right ]\]

Maple
cpu = 0.014 (sec), leaf count = 25

\[ \left \{ \left (y \relax (x ) {{\rm e}^{y \relax (x ) }}-{\it \_C1}\, \left (1+y \relax (x ) \right ) \right ) {{\rm e}^{-y \relax (x ) }}+x=0 \right \} \] 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),'implicit')

Maple raw output

(y(x)*exp(y(x))-_C1*(1+y(x)))*exp(-y(x))+x = 0