ODE
\[ y'(x)+\log \left (y'(x)\right )=x \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(x\)
Mathematica ✓
cpu = 0.157882 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \frac {1}{2} W\left (e^x\right )^2+W\left (e^x\right )+c_1\right \}\right \}\]
Maple ✓
cpu = 0.284 (sec), leaf count = 16
\[\left [y \left (x \right ) = \frac {\LambertW \left ({\mathrm e}^{x}\right )^{2}}{2}+\LambertW \left ({\mathrm e}^{x}\right )+\textit {\_C1}\right ]\] Mathematica raw input
DSolve[Log[y'[x]] + y'[x] == x,y[x],x]
Mathematica raw output
{{y[x] -> C[1] + ProductLog[E^x] + ProductLog[E^x]^2/2}}
Maple raw input
dsolve(ln(diff(y(x),x))+diff(y(x),x) = x, y(x))
Maple raw output
[y(x) = 1/2*LambertW(exp(x))^2+LambertW(exp(x))+_C1]