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 = 0.257004 (sec), leaf count = 20
\[\left \{\left \{y(x)\to \frac {x^2}{c_1 (-x)+1+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 18
\[\left [y \left (x \right ) = \frac {x^{2}}{x \textit {\_C1} -\textit {\_C1} +1}\right ]\] 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))
Maple raw output
[y(x) = x^2/(_C1*x-_C1+1)]