4.18.28 $(1-x)y(x)y^{\prime }(x)+x{y}^{\prime }(x{)}^2-y(x{)}^2=0$

ODE
$$(1-x)y(x)y^{\prime }(x)+x{y}^{\prime }(x{)}^2-y(x{)}^2=0$$ ODE Classification

[_quadrature]

Book solution method
No Missing Variables ODE, Solve for $y^{\prime }$

Mathematica ✓
cpu = 0.0040427 (sec), leaf count = 21

$$\{\{y(x)\to c_1{e}^x\},\{y(x)\to \frac{c_1}{x}\}\}$$

Maple ✓
cpu = 0.007 (sec), leaf count = 16

$$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{x},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^x\}$$ Mathematica raw input

DSolve[-y[x]^2 + (1 - x)*y[x]*y'[x] + x*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> E^x*C[1]}, {y[x] -> C[1]/x}}

Maple raw input

dsolve(x*diff(y(x),x)^2+y(x)*(1-x)*diff(y(x),x)-y(x)^2 = 0, y(x),'implicit')

Maple raw output

y(x) = _C1/x, y(x) = _C1*exp(x)