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 = 0.152578 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \frac {c_1 \left (a+b x-c_1{}^2\right )}{b}\right \}\right \}\]
Maple ✓
cpu = 0.119 (sec), leaf count = 67
\[\left [y \left (x \right ) = -\frac {2 \sqrt {3 b x +3 a}\, \left (b x +a \right )}{9 b}, y \left (x \right ) = \frac {2 \sqrt {3 b x +3 a}\, \left (b x +a \right )}{9 b}, y \left (x \right ) = x \textit {\_C1} +\frac {-\textit {\_C1}^{3}+\textit {\_C1} a}{b}\right ]\] Mathematica raw input
DSolve[b*y[x] - (a + b*x)*y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1]*(a + b*x - C[1]^2))/b}}
Maple raw input
dsolve(diff(y(x),x)^3-(b*x+a)*diff(y(x),x)+b*y(x) = 0, y(x))
Maple raw output
[y(x) = -2/9*(3*b*x+3*a)^(1/2)*(b*x+a)/b, y(x) = 2/9*(3*b*x+3*a)^(1/2)*(b*x+a)/b, y(x) = x*_C1+(-_C1^3+_C1*a)/b]