ODE
\[ (a+b x) y'(x)+c+y'(x)^2=b y(x) \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.163169 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {c+c_1 (a+b x+c_1)}{b}\right \}\right \}\]
Maple ✓
cpu = 0.03 (sec), leaf count = 50
\[\left [y \left (x \right ) = \frac {-b^{2} x^{2}-2 a b x -a^{2}+4 c}{4 b}, y \left (x \right ) = x \textit {\_C1} +\frac {\textit {\_C1}^{2}+\textit {\_C1} a +c}{b}\right ]\] Mathematica raw input
DSolve[c + (a + b*x)*y'[x] + y'[x]^2 == b*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (c + C[1]*(a + b*x + C[1]))/b}}
Maple raw input
dsolve(diff(y(x),x)^2+(b*x+a)*diff(y(x),x)+c = b*y(x), y(x))
Maple raw output
[y(x) = 1/4*(-b^2*x^2-2*a*b*x-a^2+4*c)/b, y(x) = x*_C1+(_C1^2+_C1*a+c)/b]