ODE
\[ a+x y'(x)+\log \left (y'(x)\right )=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(x\)
Mathematica ✓
cpu = 0.189092 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {1}{2} W\left (e^{-a} x\right )^2+W\left (e^{-a} x\right )+c_1\right \}\right \}\]
Maple ✓
cpu = 0.482 (sec), leaf count = 37
\[\left [y \left (x \right ) = {\mathrm e}^{a} \left (\frac {\LambertW \left (x \,{\mathrm e}^{-a}\right )^{2} {\mathrm e}^{-a}}{2}+\LambertW \left (x \,{\mathrm e}^{-a}\right ) {\mathrm e}^{-a}\right )+\textit {\_C1}\right ]\] Mathematica raw input
DSolve[a + Log[y'[x]] + x*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1] + ProductLog[x/E^a] + ProductLog[x/E^a]^2/2}}
Maple raw input
dsolve(ln(diff(y(x),x))+x*diff(y(x),x)+a = 0, y(x))
Maple raw output
[y(x) = exp(a)*(1/2*LambertW(x/exp(a))^2/exp(a)+LambertW(x/exp(a))/exp(a))+_C1]