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