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 = 0.00275505 (sec), leaf count = 12
\[\left \{\left \{y(x)\to c_1 \left (c_1+x\right )\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {\it \_C1}+x \right ) ,y \left ( x \right ) =-{\frac {{x}^{2}}{4}} \right \} \] 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),'implicit')
Maple raw output
y(x) = -1/4*x^2, y(x) = _C1*(_C1+x)