ODE
\[ a b x-a y'(x)^2+b y(x)+y'(x)^3=0 \] ODE Classification
[[_homogeneous, `class C`], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✗
cpu = 599.998 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.022 (sec), leaf count = 74
\[ \left \{ [x \left ( {\it \_T} \right ) =-{\frac {3\,{{\it \_T}}^{2}}{2\,b}}+5\,{\frac {a{\it \_T}}{b}}-5\,{\frac {{a}^{2}\ln \left ( {\it \_T}+a \right ) }{b}}+{\it \_C1},y \left ( {\it \_T} \right ) ={\frac {10\,\ln \left ( {\it \_T}+a \right ) {a}^{3}-2\,{\it \_C1}\,ab-2\,{{\it \_T}}^{3}+5\,{{\it \_T}}^{2}a-10\,{\it \_T}\,{a}^{2}}{2\,b}}] \right \} \] Mathematica raw input
DSolve[a*b*x + b*y[x] - a*y'[x]^2 + y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^3-a*diff(y(x),x)^2+b*y(x)+a*b*x = 0, y(x),'implicit')
Maple raw output
[x(_T) = -3/2/b*_T^2+5/b*a*_T-5/b*a^2*ln(_T+a)+_C1, y(_T) = 1/2*(10*ln(_T+a)*a^3-2*_C1*a*b-2*_T^3+5*_T^2*a-10*_T*a^2)/b]