4.22.13 \(8 y'(x)^3+12 y'(x)^2=27 (y(x)+x)\)

ODE
\[ 8 y'(x)^3+12 y'(x)^2=27 (y(x)+x) \] ODE Classification

[[_homogeneous, `class C`], _dAlembert]

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

Mathematica
cpu = 600.003 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 0.021 (sec), leaf count = 32

\[ \left \{ y \left ( x \right ) =-x+{\frac {4}{27}},[x \left ( {\it \_T} \right ) ={\frac {4\,{{\it \_T}}^{2}}{9}}+{\it \_C1},y \left ( {\it \_T} \right ) ={\frac {8\,{{\it \_T}}^{3}}{27}}-{\it \_C1}] \right \} \] Mathematica raw input

DSolve[12*y'[x]^2 + 8*y'[x]^3 == 27*(x + y[x]),y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(8*diff(y(x),x)^3+12*diff(y(x),x)^2 = 27*x+27*y(x), y(x),'implicit')

Maple raw output

y(x) = -x+4/27, [x(_T) = 4/9*_T^2+_C1, y(_T) = 8/27*_T^3-_C1]