Internal problem ID [4571]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12,
Miscellaneous Methods
Problem number: Exercise 12.50, page 103.
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: 0.125 (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: 2.135 (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*}