ODE
\[ a \left (\log \left (y'(x)\right )-y'(x)\right )+y(x)-x=0 \] ODE Classification
[[_homogeneous, `class C`], _dAlembert]
Book solution method
Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)
Mathematica ✓
cpu = 0.0544786 (sec), leaf count = 22
\[\left \{\left \{y(x)\to a e^{\frac {x-c_1}{a}}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) =a+x,[x \left ( {\it \_T} \right ) =a\ln \left ( {\it \_T} \right ) +{\it \_C1},y \left ( {\it \_T} \right ) =a{\it \_T}+{\it \_C1}] \right \} \] Mathematica raw input
DSolve[-x + y[x] + a*(Log[y'[x]] - y'[x]) == 0,y[x],x]
Mathematica raw output
{{y[x] -> a*E^((x - C[1])/a) + C[1]}}
Maple raw input
dsolve(a*(ln(diff(y(x),x))-diff(y(x),x))-x+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = a+x, [x(_T) = a*ln(_T)+_C1, y(_T) = _T*a+_C1]