Internal problem ID [6081]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page
198
Problem number: 1(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {{\mathrm e}^{y} \left (1+y\right ) y^{\prime }=-{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve(exp(x)+(exp(y(x))*(y(x)+1))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {LambertW}\left (-c_{1} -{\mathrm e}^{x}\right ) \]
✓ Solution by Mathematica
Time used: 60.161 (sec). Leaf size: 14
DSolve[Exp[x]+(Exp[y[x]]*(y[x]+1))*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to W\left (-e^x+c_1\right ) \]