4.11.14 \(2 x^2+x y(x) y'(x)-2 x y(x)-y(x)^2=0\)

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 = 0.0230852 (sec), leaf count = 20

\[\left \{\left \{y(x)\to x \left (W\left (e^{c_1-1} x^2\right )+1\right )\right \}\right \}\]

Maple
cpu = 0.01 (sec), leaf count = 31

\[ \left \{ {\frac {1}{2}\ln \left ({\frac {y \relax (x ) -x}{x}} \right ) }+{\frac {y \relax (x ) }{2\,x}}-\ln \relax (x ) -{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

1/2*ln((y(x)-x)/x)+1/2*y(x)/x-ln(x)-_C1 = 0