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 = 0.0412561 (sec), leaf count = 22
\[\left \{\left \{y(x)\to x e^{-a-c_1}-c_1\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) -\ln \left ( -{x}^{-1} \right ) -a+1=0,y \left ( x \right ) =\ln \left ( {\it \_C1} \right ) +{\it \_C1}\,x+a \right \} \] Mathematica raw input
DSolve[a + Log[y'[x]] + x*y'[x] == y[x],y[x],x]
Mathematica raw output
{{y[x] -> E^(-a - C[1])*x - C[1]}}
Maple raw input
dsolve(ln(diff(y(x),x))+x*diff(y(x),x)+a = y(x), y(x),'implicit')
Maple raw output
y(x)-ln(-1/x)-a+1 = 0, y(x) = ln(_C1)+_C1*x+a