49.22.12 problem 2(d)

Internal problem ID [7758]
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)
Date solved : Monday, January 27, 2025 at 03:12:08 PM
CAS classification : [_quadrature]

\begin{align*} {\mathrm e}^{y}+x \,{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \end{align*}

✓ 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)
 

\[ y = -x -\ln \left (x \right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 16

DSolve[(Exp[y[x]]+x*Exp[y[x]])+(x*Exp[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x-\log (x)-1+c_1 \]