ODE
\[ y'(x)^2+x y'(x)-y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.154402 (sec), leaf count = 12
\[\{\{y(x)\to c_1 (x+c_1)\}\}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 19
\[\left [y \left (x \right ) = -\frac {x^{2}}{4}, y \left (x \right ) = \textit {\_C1}^{2}+x \textit {\_C1}\right ]\] Mathematica raw input
DSolve[-y[x] + x*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*(x + C[1])}}
Maple raw input
dsolve(diff(y(x),x)^2+x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = -1/4*x^2, y(x) = _C1^2+_C1*x]