ODE
\[ 2 x^2+x y(x) y'(x)-2 x y(x)-y(x)^2=0 \] ODE Classification
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.259173 (sec), leaf count = 20
\[\left \{\left \{y(x)\to x \left (1+W\left (e^{-1+c_1} x^2\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.194 (sec), leaf count = 29
\[[y \left (x \right ) = {\mathrm e}^{-\LambertW \left ({\mathrm e}^{2 \textit {\_C1}} {\mathrm e}^{-1} x^{2}\right )+2 \textit {\_C1} -1} x^{3}+x]\] Mathematica raw input
DSolve[2*x^2 - 2*x*y[x] - y[x]^2 + x*y[x]*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*(1 + ProductLog[E^(-1 + C[1])*x^2])}}
Maple raw input
dsolve(x*y(x)*diff(y(x),x)+2*x^2-2*x*y(x)-y(x)^2 = 0, y(x))
Maple raw output
[y(x) = exp(-LambertW(exp(_C1)^2*exp(-1)*x^2)+2*_C1-1)*x^3+x]