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

ODE
\[ x^2 (1-y(x)) y'(x)+(x+1) y(x)^2=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0184982 (sec), leaf count = 25

\[\left \{\left \{y(x)\to -\frac {1}{W\left (-\frac {e^{\frac {1}{x}-c_1}}{x}\right )}\right \}\right \}\]

Maple
cpu = 0.011 (sec), leaf count = 23

\[ \left \{ -{x}^{-1}+\ln \relax (x ) - \left (y \relax (x ) \right ) ^{-1}-\ln \left (y \relax (x ) \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[(1 + x)*y[x]^2 + x^2*(1 - y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -ProductLog[-(E^(x^(-1) - C[1])/x)]^(-1)}}

Maple raw input

dsolve(x^2*(1-y(x))*diff(y(x),x)+(1+x)*y(x)^2 = 0, y(x),'implicit')

Maple raw output

-1/x+ln(x)-1/y(x)-ln(y(x))+_C1 = 0