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 = 0.224491 (sec), leaf count = 22
\[\left \{\left \{y(x)\to a e^{\frac {x-c_1}{a}}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.711 (sec), leaf count = 45
\[\left [y \left (x \right ) = a +x, y \left (x \right ) = -a \left (\ln \left ({\mathrm e}^{-\frac {\textit {\_C1}}{a}+\frac {x}{a}}\right )-{\mathrm e}^{-\frac {\textit {\_C1}}{a}+\frac {x}{a}}\right )+x\right ]\] 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))
Maple raw output
[y(x) = a+x, y(x) = -a*(ln(exp(-1/a*_C1+1/a*x))-exp(-1/a*_C1+1/a*x))+x]