4.21.41 $-axy(x)y^{\prime }(x)+2ay(x{)}^2+y^{\prime }(x{)}^3=0$

ODE
$$-axy(x)y^{\prime }(x)+2ay(x{)}^2+y^{\prime }(x{)}^3=0$$ ODE Classification

[[_1st_order, _with_linear_symmetries]]

Book solution method
No Missing Variables ODE, Solve for $x$

Mathematica ✗
cpu = 599.997 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 1.507 (sec), leaf count = 38

$$\{y\left(x\right)=\frac{a{x}^3}{27},[x\left(\mathit{\_}\mathit{T}\right)=\frac{2{\mathit{\_}\mathit{C}\mathit{1}}^2\mathit{\_}\mathit{T}a+1}{\mathit{\_}\mathit{C}\mathit{1}a},y\left(\mathit{\_}\mathit{T}\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{T}}^2]\}$$ Mathematica raw input

DSolve[2*a*y[x]^2 - a*x*y[x]*y'[x] + y'[x]^3 == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(diff(y(x),x)^3-a*x*y(x)*diff(y(x),x)+2*a*y(x)^2 = 0, y(x),'implicit')

Maple raw output

y(x) = 1/27*a*x^3, [x(_T) = (2*_C1^2*_T*a+1)/a/_C1, y(_T) = _C1*_T^2]