ODE
\[ -2 a x^3 y'(x)+4 a x^2 y(x)+y'(x)^2=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
Change of variable
Mathematica ✗
cpu = 599.998 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.403 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( a{x}^{2}-{\it \_C1} \right ) }{a}},y \left ( x \right ) ={\frac {a{x}^{4}}{4}} \right \} \] Mathematica raw input
DSolve[4*a*x^2*y[x] - 2*a*x^3*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^2-2*a*x^3*diff(y(x),x)+4*a*x^2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = 1/4*a*x^4, y(x) = _C1*(a*x^2-_C1)/a