4.11.20 \((x y(x)+1) y'(x)+y(x)^2=0\)

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 = 0.0142415 (sec), leaf count = 16

\[\left \{\left \{y(x)\to \frac {W\left (e^{c_1} x\right )}{x}\right \}\right \}\]

Maple
cpu = 0.02 (sec), leaf count = 17

\[ \left \{ x+{\frac {\ln \left (y \relax (x ) \right ) -{\it \_C1}}{y \relax (x ) }}=0 \right \} \] 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),'implicit')

Maple raw output

x+(ln(y(x))-_C1)/y(x) = 0