Internal problem ID [4488]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {{\mathrm e}^{x +y}}{y-1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 11
dsolve(diff(y(x),x)=exp(x+y(x))/(y(x)-1),y(x), singsol=all)
\[ y \relax (x ) = -\LambertW \left ({\mathrm e}^{x}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 60.23 (sec). Leaf size: 14
DSolve[y'[x]==Exp[x+y[x]]/(y[x]-1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ProductLog}\left (e^x+c_1\right ) \\ \end{align*}