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 = 1.46516 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \frac {-a+c_1 (-2 x+c_1)}{x}\right \}\right \}\]
Maple ✓
cpu = 0.577 (sec), leaf count = 32
\[\left [y \left (x \right ) = -\frac {x^{2}+a}{x}, y \left (x \right ) = \textit {\_C1} +\frac {\frac {\textit {\_C1}^{2}}{4}-a}{x}\right ]\] 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))
Maple raw output
[y(x) = -(x^2+a)/x, y(x) = _C1+(1/4*_C1^2-a)/x]