4.24.3 $a+x{y}^{\prime }(x)+\log (y^{\prime }(x))=y(x)$

ODE
$$a+x{y}^{\prime }(x)+\log (y^{\prime }(x))=y(x)$$ 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

$$\left\{\{y(x)\to x{e}^{-a-c_1}-c_1\}\right\}$$

Maple ✓
cpu = 0.019 (sec), leaf count = 28

$$\{y\left(x\right)-\ln (-x^{-1})-a+1=0,y\left(x\right)=\ln \left(\mathit{\_}\mathit{C}\mathit{1}\right)+\mathit{\_}\mathit{C}\mathit{1}x+a\}$$ 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