ODE
\[ 12 x^3+x y'(x)^4-2 y(x) y'(x)^3=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✗
cpu = 599.998 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 2.01 (sec), leaf count = 35
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{4}-{\frac {64\,{x}^{6}}{9}}=0,[y \left ( {\it \_T} \right ) ={\frac { \left ( 12\,{{\it \_C1}}^{2}+{{\it \_T}}^{2} \right ) {\it \_C1}}{2}},x \left ( {\it \_T} \right ) ={\it \_C1}\,{\it \_T}] \right \} \] Mathematica raw input
DSolve[12*x^3 - 2*y[x]*y'[x]^3 + x*y'[x]^4 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(x*diff(y(x),x)^4-2*y(x)*diff(y(x),x)^3+12*x^3 = 0, y(x),'implicit')
Maple raw output
y(x)^4-64/9*x^6 = 0, [y(_T) = 1/2*(12*_C1^2+_T^2)*_C1, x(_T) = _C1*_T]