ODE
\[ a \left (x y'(x)-y(x)\right )+\log \left (y'(x)\right )=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, \(f(y-x y', y')=0\)
Mathematica ✓
cpu = 0.151477 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \frac {\log (c_1)}{a}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.156 (sec), leaf count = 36
\[\left [y \left (x \right ) = \frac {\ln \left (-\frac {1}{a x}\right )}{a}-\frac {1}{a}, y \left (x \right ) = \textit {\_C1} x +\frac {\ln \left (\textit {\_C1} \right )}{a}\right ]\] Mathematica raw input
DSolve[Log[y'[x]] + a*(-y[x] + x*y'[x]) == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + Log[C[1]]/a}}
Maple raw input
dsolve(ln(diff(y(x),x))+a*(x*diff(y(x),x)-y(x)) = 0, y(x))
Maple raw output
[y(x) = 1/a*ln(-1/a/x)-1/a, y(x) = _C1*x+ln(_C1)/a]