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 = 0.0149661 (sec), leaf count = 22
\[\left \{\left \{y(x)\to c_1+\frac {1}{2} W\left (e^x\right )^2+W\left (e^x\right )\right \}\right \}\]
Maple ✓
cpu = 0.06 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={\frac { \left ( {\it lambertW} \left ( {{\rm e}^{x}} \right ) \right ) ^{2}}{2}}+{\it lambertW} \left ( {{\rm e}^{x}} \right ) +{\it \_C1} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/2*LambertW(exp(x))^2+LambertW(exp(x))+_C1