4.8.17 \((1-x) x^2 y'(x)=(2-x) x y(x)-y(x)^2\)

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

[[_homogeneous, `class D`], _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.0139954 (sec), leaf count = 20

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

Maple
cpu = 0.012 (sec), leaf count = 22

\[ \left \{ -{\frac { \left (-1+x \right ) {\it \_C1}}{{x}^{2}}}+ \left (y \relax (x ) \right ) ^{-1}-{x}^{-2}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> x^2/(1 + C[1] - x*C[1])}}

Maple raw input

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

Maple raw output

-1/x^2*(-1+x)*_C1+1/y(x)-1/x^2 = 0