ODE
\[ a+x y'(x)+\log \left (y'(x)\right )=y(x) \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.154956 (sec), leaf count = 14
\[\{\{y(x)\to a+c_1 x+\log (c_1)\}\}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 23
\[\left [y \left (x \right ) = \ln \left (-\frac {1}{x}\right )+a -1, y \left (x \right ) = \ln \left (\textit {\_C1} \right )+\textit {\_C1} x +a\right ]\] Mathematica raw input
DSolve[a + Log[y'[x]] + x*y'[x] == y[x],y[x],x]
Mathematica raw output
{{y[x] -> a + x*C[1] + Log[C[1]]}}
Maple raw input
dsolve(ln(diff(y(x),x))+x*diff(y(x),x)+a = y(x), y(x))
Maple raw output
[y(x) = ln(-1/x)+a-1, y(x) = ln(_C1)+_C1*x+a]