ODE
\[ \sqrt {a^2+b^2 y'(x)^2}+x y'(x)-y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✗
cpu = 600.125 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.032 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) =\sqrt {{b}^{2}{{\it \_C1}}^{2}+{a}^{2}}+{\it \_C1}\,x \right \} \] Mathematica raw input
DSolve[-y[x] + x*y'[x] + Sqrt[a^2 + b^2*y'[x]^2] == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve((a^2+b^2*diff(y(x),x)^2)^(1/2)+x*diff(y(x),x)-y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C1^2*b^2+a^2)^(1/2)+_C1*x