ODE
\[ a x y'(x)-a y(x)+y'(x)^3=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.149384 (sec), leaf count = 18
\[\left \{\left \{y(x)\to \frac {c_1{}^3}{a}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.073 (sec), leaf count = 39
\[\left [y \left (x \right ) = -\frac {2 \sqrt {-3 a x}\, x}{9}, y \left (x \right ) = \frac {2 \sqrt {-3 a x}\, x}{9}, y \left (x \right ) = x \textit {\_C1} +\frac {\textit {\_C1}^{3}}{a}\right ]\] Mathematica raw input
DSolve[-(a*y[x]) + a*x*y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + C[1]^3/a}}
Maple raw input
dsolve(diff(y(x),x)^3+a*x*diff(y(x),x)-a*y(x) = 0, y(x))
Maple raw output
[y(x) = -2/9*(-3*a*x)^(1/2)*x, y(x) = 2/9*(-3*a*x)^(1/2)*x, y(x) = x*_C1+_C1^3/a]