ODE
\[ (x y(x)+1) y'(x)+y(x)^2=0 \] ODE Classification
[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.276668 (sec), leaf count = 16
\[\left \{\left \{y(x)\to \frac {W\left (e^{c_1} x\right )}{x}\right \}\right \}\]
Maple ✓
cpu = 0.061 (sec), leaf count = 14
\[[y \left (x \right ) = {\mathrm e}^{-\LambertW \left (x \,{\mathrm e}^{\textit {\_C1}}\right )+\textit {\_C1}}]\] Mathematica raw input
DSolve[y[x]^2 + (1 + x*y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ProductLog[E^C[1]*x]/x}}
Maple raw input
dsolve((1+x*y(x))*diff(y(x),x)+y(x)^2 = 0, y(x))
Maple raw output
[y(x) = exp(-LambertW(x*exp(_C1))+_C1)]