ODE
\[ x^2 y'(x)^2-x (x-2 y(x)) y'(x)+y(x)^2=0 \] ODE Classification
[[_homogeneous, `class A`], _rational, _dAlembert]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.276862 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {e^{-4 c_1}-2 i e^{-2 c_1} x}{4 x}\right \}\right \}\]
Maple ✓
cpu = 9.203 (sec), leaf count = 33
\[\left [y \left (x \right ) = \frac {x}{4}, y \left (x \right ) = -\frac {\textit {\_C1} \left (-x +\textit {\_C1} \right )}{x}, y \left (x \right ) = -\frac {\textit {\_C1} \left (x +\textit {\_C1} \right )}{x}\right ]\] Mathematica raw input
DSolve[y[x]^2 - x*(x - 2*y[x])*y'[x] + x^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^(-4*C[1]) - ((2*I)*x)/E^(2*C[1]))/(4*x)}}
Maple raw input
dsolve(x^2*diff(y(x),x)^2-x*(x-2*y(x))*diff(y(x),x)+y(x)^2 = 0, y(x))
Maple raw output
[y(x) = 1/4*x, y(x) = -_C1*(-x+_C1)/x, y(x) = -_C1*(x+_C1)/x]