7.5.30 problem 30

Internal problem ID [134]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 30
Date solved : Friday, February 07, 2025 at 07:56:18 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} \left (x +{\mathrm e}^{y}\right ) y^{\prime }&=x \,{\mathrm e}^{-y}-1 \end{align*}

✓ Solution by Maple

Time used: 0.645 (sec). Leaf size: 37

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

\begin{align*} y &= \ln \left (-x -\sqrt {2 x^{2}+c_1}\right ) \\ y &= \ln \left (-x +\sqrt {2 x^{2}+c_1}\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.709 (sec). Leaf size: 52

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

\begin{align*} y(x)\to \log \left (-x-\sqrt {2} \sqrt {x^2+c_1}\right ) \\ y(x)\to \log \left (-x+\sqrt {2} \sqrt {x^2+c_1}\right ) \\ \end{align*}