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 = 0.156383 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \sqrt {a^2+b^2 c_1{}^2}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.091 (sec), leaf count = 21
\[\left [y \left (x \right ) = \sqrt {b^{2} \textit {\_C1}^{2}+a^{2}}+\textit {\_C1} x\right ]\] Mathematica raw input
DSolve[-y[x] + x*y'[x] + Sqrt[a^2 + b^2*y'[x]^2] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + Sqrt[a^2 + b^2*C[1]^2]}}
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))
Maple raw output
[y(x) = (_C1^2*b^2+a^2)^(1/2)+_C1*x]