Internal problem ID [7656]
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]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{-y+x}+{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.24 (sec). Leaf size: 20
dsolve(diff(y(x),x) - exp(x-y(x)) + exp(x)=0,y(x), singsol=all)
\[ y \relax (x ) = -{\mathrm e}^{x}+\ln \left (-1+{\mathrm e}^{{\mathrm e}^{x}+c_{1}}\right )-c_{1} \]
✓ Solution by Mathematica
Time used: 0.45 (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*}