ODE
\[ a \sqrt {y'(x)^2+1}+x y'(x)-y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.15129 (sec), leaf count = 22
\[\left \{\left \{y(x)\to a \sqrt {1+c_1{}^2}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.061 (sec), leaf count = 17
\[\left [y \left (x \right ) = a \sqrt {\textit {\_C1}^{2}+1}+\textit {\_C1} x\right ]\] Mathematica raw input
DSolve[-y[x] + x*y'[x] + a*Sqrt[1 + y'[x]^2] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + a*Sqrt[1 + C[1]^2]}}
Maple raw input
dsolve(a*(1+diff(y(x),x)^2)^(1/2)+x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = a*(_C1^2+1)^(1/2)+_C1*x]