ODE
\[ y'(x)^2+x y'(x)-y(x)+x=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _dAlembert]
Book solution method
Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)
Mathematica ✓
cpu = 1.74029 (sec), leaf count = 6
\[\{\{y(x)\to 1\}\}\]
Maple ✓
cpu = 0.045 (sec), leaf count = 39
\[\left [y \left (x \right ) = \left (2+\LambertW \left (\frac {\textit {\_C1} \,{\mathrm e}^{\frac {x}{2}-1}}{2}\right )-\frac {x}{2}\right ) x +\left (\LambertW \left (\frac {\textit {\_C1} \,{\mathrm e}^{\frac {x}{2}-1}}{2}\right )-\frac {x}{2}+1\right )^{2}\right ]\] Mathematica raw input
DSolve[x - y[x] + x*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> 1}}
Maple raw input
dsolve(diff(y(x),x)^2+x*diff(y(x),x)+x-y(x) = 0, y(x))
Maple raw output
[y(x) = (2+LambertW(1/2*_C1*exp(1/2*x-1))-1/2*x)*x+(LambertW(1/2*_C1*exp(1/2*x-1))-1/2*x+1)^2]