4.18.48 $x^2{y}^{\prime }(x{)}^2=(x-y(x){)}^2$

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

[_linear]

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

Mathematica ✓
cpu = 0.0051665 (sec), leaf count = 30

$$\{\{y(x)\to \frac{c_1}{x}+\frac{x}{2}\},\{y(x)\to x(c_1-\log (x))\}\}$$

Maple ✓
cpu = 0.012 (sec), leaf count = 24

$$\{y\left(x\right)=(-\ln \left(x\right)+\mathit{\_}\mathit{C}\mathit{1})x,y\left(x\right)=\frac{x}{2}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}\}$$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> x/2 + C[1]/x}, {y[x] -> x*(C[1] - Log[x])}}

Maple raw input

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

Maple raw output

y(x) = (-ln(x)+_C1)*x, y(x) = 1/2*x+1/x*_C1