ODE
\[ y(x)^4 y'(x)^3-6 x y'(x)+2 y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✗
cpu = 599.999 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.366 (sec), leaf count = 40
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{6}-8\,{x}^{3}=0,[x \left ( {\it \_T} \right ) ={\frac {{\it \_C1}}{6} \left ( {{\it \_C1}}^{3}{{\it \_T}}^{{\frac {3}{2}}}+2 \right ) {{\it \_T}}^{-{\frac {3}{2}}}},y \left ( {\it \_T} \right ) ={{\it \_C1}{\frac {1}{\sqrt {{\it \_T}}}}}] \right \} \] Mathematica raw input
DSolve[2*y[x] - 6*x*y'[x] + y[x]^4*y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(y(x)^4*diff(y(x),x)^3-6*x*diff(y(x),x)+2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x)^6-8*x^3 = 0, [x(_T) = 1/6*(_C1^3*_T^(3/2)+2)*_C1/_T^(3/2), y(_T) = _C1/_T^(1/2)]