36.4.1 problem 1

Internal problem ID [6339]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Review problems. page 79
Problem number : 1
Date solved : Monday, January 27, 2025 at 01:57:31 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x +y}}{y-1} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 11

dsolve(diff(y(x),x)=exp(x+y(x))/(y(x)-1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 60.153 (sec). Leaf size: 14

DSolve[D[y[x],x]==Exp[x+y[x]]/(y[x]-1),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -W\left (e^x+c_1\right ) \]