ODE
\[ -(x+1) y'(x)+y'(x) \log \left (y'(x)\right )+y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.162785 (sec), leaf count = 16
\[\{\{y(x)\to c_1 (x+1-\log (c_1))\}\}\]
Maple ✓
cpu = 0.265 (sec), leaf count = 19
\[[y \left (x \right ) = {\mathrm e}^{x}, y \left (x \right ) = \textit {\_C1} x -\textit {\_C1} \ln \left (\textit {\_C1} \right )+\textit {\_C1}]\] Mathematica raw input
DSolve[y[x] - (1 + x)*y'[x] + Log[y'[x]]*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*(1 + x - Log[C[1]])}}
Maple raw input
dsolve(diff(y(x),x)*ln(diff(y(x),x))-(x+1)*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = exp(x), y(x) = _C1*x-_C1*ln(_C1)+_C1]