ODE
\[ (a-x) y'(x)^2-b+y(x) y'(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, \(f(y-x y', y')=0\)
Mathematica ✓
cpu = 0.159303 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_1 (x-a)+\frac {b}{c_1}\right \}\right \}\]
Maple ✓
cpu = 0.082 (sec), leaf count = 50
\[\left [y \left (x \right ) = -2 \sqrt {-a b +b x}, y \left (x \right ) = 2 \sqrt {-a b +b x}, y \left (x \right ) = x \textit {\_C1} +\frac {-a \,\textit {\_C1}^{2}+b}{\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[-b + y[x]*y'[x] + (a - x)*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> b/C[1] + (-a + x)*C[1]}}
Maple raw input
dsolve((a-x)*diff(y(x),x)^2+y(x)*diff(y(x),x)-b = 0, y(x))
Maple raw output
[y(x) = -2*(-a*b+b*x)^(1/2), y(x) = 2*(-a*b+b*x)^(1/2), y(x) = x*_C1+(-_C1^2*a+b)/_C1]