34.2.1 problem 1

Internal problem ID [6031]
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
Date solved : Monday, January 27, 2025 at 01:33:55 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

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

\[ y = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-x}}{c_1 x}\right ) \]

✓ Solution by Mathematica

Time used: 4.161 (sec). Leaf size: 28

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