ODE
\[ -(a+b x) y'(x)+b y(x)+y'(x)^3=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✗
cpu = 600.013 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.093 (sec), leaf count = 45
\[ \left \{ {\frac {27\,{b}^{2} \left ( y \left ( x \right ) \right ) ^{2}-4\, \left ( bx+a \right ) ^{3}}{27\,{b}^{2}}}=0,y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( -{{\it \_C1}}^{2}+bx+a \right ) }{b}} \right \} \] Mathematica raw input
DSolve[b*y[x] - (a + b*x)*y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^3-(b*x+a)*diff(y(x),x)+b*y(x) = 0, y(x),'implicit')
Maple raw output
1/27*(27*b^2*y(x)^2-4*(b*x+a)^3)/b^2 = 0, y(x) = _C1*(-_C1^2+b*x+a)/b