ODE
\[ x^2 y'(x)^2-x y'(x)+(1-y(x)) y(x)=0 \] ODE Classification
[_separable]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.181804 (sec), leaf count = 21
\[\left \{\{y(x)\to c_1 x\},\left \{y(x)\to \frac {x+c_1}{x}\right \}\right \}\]
Maple ✓
cpu = 0.05 (sec), leaf count = 17
\[\left [y \left (x \right ) = x \textit {\_C1}, y \left (x \right ) = \frac {x +\textit {\_C1}}{x}\right ]\] Mathematica raw input
DSolve[(1 - y[x])*y[x] - x*y'[x] + x^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1]}, {y[x] -> (x + C[1])/x}}
Maple raw input
dsolve(x^2*diff(y(x),x)^2-x*diff(y(x),x)+y(x)*(1-y(x)) = 0, y(x))
Maple raw output
[y(x) = x*_C1, y(x) = (x+_C1)/x]