Internal problem ID [108]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left ({\mathrm e}^{y}+x \right ) y^{\prime }+1-x \,{\mathrm e}^{-y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (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 \relax (x ) = \ln \left (-x -\sqrt {2 x^{2}+c_{1}}\right ) \\ y \relax (x ) = \ln \left (-x +\sqrt {2 x^{2}+c_{1}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.953 (sec). Leaf size: 52
DSolve[(Exp[y[x]]+x)*y'[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*}