ODE
\[ -a x y(x) y'(x)+2 a y(x)^2+y'(x)^3=0 \] 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
\[ \left \{ y \left ( x \right ) ={\frac {a{x}^{3}}{27}},[x \left ( {\it \_T} \right ) ={\frac {2\,{{\it \_C1}}^{2}{\it \_T}\,a+1}{{\it \_C1}\,a}},y \left ( {\it \_T} \right ) ={\it \_C1}\,{{\it \_T}}^{2}] \right \} \] 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]