4.18.50 \(x^2 y'(x)^2-x y'(x)+(1-y(x)) y(x)=0\)

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 = 0.0045838 (sec), leaf count = 21

\[\left \{\left \{y(x)\to c_1 x\right \},\left \{y(x)\to \frac {c_1+x}{x}\right \}\right \}\]

Maple
cpu = 0.01 (sec), leaf count = 17

\[ \left \{ y \relax (x ) ={\it \_C1}\,x,y \relax (x ) ={\frac {x+{\it \_C1}}{x}} \right \} \] 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),'implicit')

Maple raw output

y(x) = _C1*x, y(x) = (x+_C1)/x