ODE
\[ y'(x)^2-(x+1) y'(x)+y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.145776 (sec), leaf count = 15
\[\{\{y(x)\to c_1 (x+1-c_1)\}\}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 27
\[\left [y \left (x \right ) = \frac {1}{4} x^{2}+\frac {1}{2} x +\frac {1}{4}, y \left (x \right ) = -\textit {\_C1}^{2}+x \textit {\_C1} +\textit {\_C1}\right ]\] Mathematica raw input
DSolve[y[x] - (1 + x)*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (1 + x - C[1])*C[1]}}
Maple raw input
dsolve(diff(y(x),x)^2-(x+1)*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = 1/4*x^2+1/2*x+1/4, y(x) = -_C1^2+_C1*x+_C1]