4.22.20 \(8 x y'(x)^3-12 y(x) y'(x)^2+9 y(x)=0\)

ODE
\[ 8 x y'(x)^3-12 y(x) y'(x)^2+9 y(x)=0 \] ODE Classification

[[_1st_order, _with_linear_symmetries], _dAlembert]

Book solution method
No Missing Variables ODE, Solve for \(x\)

Mathematica ✗
cpu = 600.002 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 0.032 (sec), leaf count = 56

\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}-{\frac {9\,{x}^{2}}{4}}=0,y \left ( x \right ) =0,[x \left ( {\it \_T} \right ) =4\,{\it \_C1}\,{{\it \_T}}^{2}-3\,{\it \_C1},y \left ( {\it \_T} \right ) =8\,{\frac { \left ( 4\,{{\it \_T}}^{2}-3 \right ) {\it \_C1}\,{{\it \_T}}^{3}}{12\,{{\it \_T}}^{2}-9}}] \right \} \] Mathematica raw input

DSolve[9*y[x] - 12*y[x]*y'[x]^2 + 8*x*y'[x]^3 == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(8*x*diff(y(x),x)^3-12*y(x)*diff(y(x),x)^2+9*y(x) = 0, y(x),'implicit')

Maple raw output

y(x)^2-9/4*x^2 = 0, y(x) = 0, [x(_T) = 4*_C1*_T^2-3*_C1, y(_T) = 8*(4*_T^2-3)*_C
1*_T^3/(12*_T^2-9)]