Internal problem ID [8412]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 75.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-{\mathrm e}^{-y+x}=-{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 20
dsolve(diff(y(x),x) - exp(x-y(x)) + exp(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{x}+\ln \left (-1+{\mathrm e}^{{\mathrm e}^{x}+c_{1}}\right )-c_{1} \]
✓ Solution by Mathematica
Time used: 2.171 (sec). Leaf size: 23
DSolve[y'[x] - Exp[x-y[x]] + Exp[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (1+e^{-e^x+c_1}\right ) y(x)\to 0 \end{align*}