Internal problem ID [4179]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter 2, Equations of the first order and degree. page 20
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x +1\right ) y+\left (1-y\right ) x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 19
dsolve((1+x)*y(x)+(1-y(x))*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\LambertW \left (-\frac {{\mathrm e}^{-x}}{c_{1} x}\right ) \]
✓ Solution by Mathematica
Time used: 60.035 (sec). Leaf size: 23
DSolve[(1+x)*y[x]+(1-y[x])*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*}