62.12.19 problem Ex 20

Internal problem ID [12865]
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
Date solved : Tuesday, January 28, 2025 at 04:29:04 AM
CAS classification : [_separable]

\begin{align*} \left (1-x \right ) y-\left (y+1\right ) x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 2.095 (sec). Leaf size: 21

DSolve[(1-x)*y[x]-(1+y[x])*x*D[y[x],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*}