Internal problem ID [3263]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 519.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(x*(1-y(x))*diff(y(x),x)+(1+x)*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\LambertW \left (-\frac {{\mathrm e}^{-x}}{c_{1} x}\right ) \]
✓ Solution by Mathematica
Time used: 60.028 (sec). Leaf size: 23
DSolve[x(1-y[x])y'[x]+(1+x)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ProductLog}\left (-\frac {e^{-x-c_1}}{x}\right ) \\ \end{align*}