8.5.30 problem 30

Internal problem ID [758]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 30
Date solved : Monday, January 27, 2025 at 03:03:29 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 37

dsolve((exp(y(x))+x)*diff(y(x),x) = -1+x/exp(y(x)),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: 2.591 (sec). Leaf size: 52

DSolve[(Exp[y[x]]+x)*D[y[x],x]== -1+x/Exp[y[x]],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*}