Internal problem ID [11189]
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]
\[ \boxed {\left (1-x \right ) y-\left (y+1\right ) x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve((1-x)*y(x)-(1+y(x))*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {LambertW}\left (\frac {{\mathrm e}^{-x} x}{c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 5.134 (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 W\left (x e^{-x+c_1}\right ) \\ y(x)\to 0 \\ \end{align*}