Internal problem ID [4355]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 1.1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x +1\right ) y+\left (1-y\right ) x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve((1+x)*y(x)+(1-y(x))*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-x}}{c_{1} x}\right ) \]
✓ Solution by Mathematica
Time used: 3.139 (sec). Leaf size: 28
DSolve[(1+x)*y[x]+(1-y[x])*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -W\left (-\frac {e^{-x-c_1}}{x}\right ) y(x)\to 0 \end{align*}