6.50 problem Exercise 12.50, page 103

Internal problem ID [4063]

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]

Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}=0} \end {gather*}

Solution by Maple

Time used: 0.156 (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*}