Internal problem ID [5337]
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: 2(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {{\mathrm e}^{y}+x \,{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 13
dsolve((exp(y(x))+x*exp(y(x)))+(x*exp(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -x -\ln \relax (x )+c_{1} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 15
DSolve[(Exp[y[x]]+x*Exp[y[x]])+(x*Exp[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\log (x)+c_1 \\ \end{align*}