4.17.9 $-2a{x}^3{y}^{\prime }(x)+4a{x}^{2}y(x)+y^{\prime }(x{)}^2=0$

ODE
$$-2a{x}^3{y}^{\prime }(x)+4a{x}^{2}y(x)+y^{\prime }(x{)}^2=0$$ 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

$$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}(a{x}^2-\mathit{\_}\mathit{C}\mathit{1})}{a},y\left(x\right)=\frac{a{x}^4}{4}\}$$ 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