ODE
\[ -4 a+x^2 y'(x)^2+2 x (y(x)+2 x) y'(x)+y(x)^2=0 \] ODE Classification
[[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.498384 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \frac {c_1 \left (c_1-2 x\right )-a}{x}\right \}\right \}\]
Maple ✓
cpu = 0.231 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) ={\frac {-{x}^{2}-a}{x}},y \left ( x \right ) ={\it \_C1}+{\frac {{{\it \_C1}}^{2}-4\,a}{4\,x}} \right \} \] Mathematica raw input
DSolve[-4*a + y[x]^2 + 2*x*(2*x + y[x])*y'[x] + x^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-a + C[1]*(-2*x + C[1]))/x}}
Maple raw input
dsolve(x^2*diff(y(x),x)^2+2*x*(2*x+y(x))*diff(y(x),x)-4*a+y(x)^2 = 0, y(x),'implicit')
Maple raw output
y(x) = (-x^2-a)/x, y(x) = _C1+1/4*(_C1^2-4*a)/x