12.19 problem Ex 20

Internal problem ID [10175]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number: Ex 20.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {\left (1-x \right ) y-\left (y+1\right ) x y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 14

dsolve((1-x)*y(x)-(1+y(x))*x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = \LambertW \left (\frac {{\mathrm e}^{-x} x}{c_{1}}\right ) \]

Solution by Mathematica

Time used: 18.346 (sec). Leaf size: 21

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 (x e^{-x+c_1}\right ) \\ y(x)\to 0 \\ \end{align*}