ODE
\[ f\left (x y'(x)^2\right )=y(x)-2 x y'(x) \] ODE Classification
[`y=_G(x,y')`]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.0170185 (sec), leaf count = 42
\[\left \{\left \{y(x)\to f\left (c_1\right )-2 \sqrt {c_1} \sqrt {x},y(x)\to f\left (c_1\right )+2 \sqrt {c_1} \sqrt {x}\right \}\right \}\]
Maple ✓
cpu = 0.295 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) =f \left ( {\frac {{{\it \_C1}}^{2}}{4}} \right ) +\sqrt {x}{\it \_C1} \right \} \] Mathematica raw input
DSolve[f[x*y'[x]^2] == y[x] - 2*x*y'[x],y[x],x]
Mathematica raw output
{{y[x] -> -2*Sqrt[x]*Sqrt[C[1]] + f[C[1]], y[x] -> 2*Sqrt[x]*Sqrt[C[1]] + f[C[1]]}}
Maple raw input
dsolve(f(x*diff(y(x),x)^2) = y(x)-2*x*diff(y(x),x), y(x),'implicit')
Maple raw output
y(x) = f(1/4*_C1^2)+x^(1/2)*_C1