ODE
\[ a y(x)+y'(x)^3-x y'(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✗
cpu = 602.979 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.021 (sec), leaf count = 108
\[ \left \{ [x \left ( {\it \_T} \right ) ={{\it \_T}}^{{\frac {1}{a} \left ( 1-{a}^{-1} \right ) ^{-1}}} \left ( -3\,{\frac {{{\it \_T}}^{2}}{{{\it \_T}}^{ \left ( a-1 \right ) ^{-1}} \left ( 2\,a-3 \right ) }}+{\it \_C1} \right ) ,y \left ( {\it \_T} \right ) =-2\,{\frac { \left ( \left ( {{\it \_T}}^{2}-{\it \_C1}\,{{\it \_T}}^{ \left ( a-1 \right ) ^{-1}} \right ) \left ( a-3/2 \right ) {{\it \_T}}^{ \left ( a-1 \right ) ^{-1}}+3/2\,{{\it \_T}}^{ \left ( a-1 \right ) ^{-1}}{{\it \_T}}^{2} \right ) {\it \_T}}{ \left ( 2\,{a}^{2}-3\,a \right ) {{\it \_T}}^{ \left ( a-1 \right ) ^{-1}}}}] \right \} \] Mathematica raw input
DSolve[a*y[x] - x*y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^3-x*diff(y(x),x)+a*y(x) = 0, y(x),'implicit')
Maple raw output
[x(_T) = _T^(1/a/(1-1/a))*(-3/(_T^(1/(a-1)))*_T^2/(2*a-3)+_C1), y(_T) = -2*((_T^2-_C1*_T^(1/(a-1)))*(a-3/2)*_T^(1/(a-1))+3/2*_T^(1/(a-1))*_T^2)*_T/(2*a^2-3*a)/(_T^(1/(a-1)))]