Internal problem ID [3827]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1143.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\ln \left (y^{\prime }\right )+x y^{\prime }+a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 24
dsolve(ln(diff(y(x),x))+x*diff(y(x),x)+a = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\LambertW \left (x \,{\mathrm e}^{-a}\right )^{2}}{2}+\LambertW \left (x \,{\mathrm e}^{-a}\right )+c_{1} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 30
DSolve[Log[y'[x]]+x y'[x]+ a ==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \text {ProductLog}\left (e^{-a} x\right )^2+\text {ProductLog}\left (e^{-a} x\right )+c_1 \\ \end{align*}