32.6.50 problem Exercise 12.50, page 103

Internal problem ID [5915]
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
Date solved : Monday, January 27, 2025 at 01:27:22 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.224 (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: 2.226 (sec). Leaf size: 23

DSolve[D[y[x],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*}