47.1.21 problem 21

Internal problem ID [7402]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 21
Date solved : Monday, January 27, 2025 at 02:52:49 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 9

dsolve(diff(y(x),x)=exp(x-y(x)),y(x), singsol=all)
 

\[ y = \ln \left (c_{1} +{\mathrm e}^{x}\right ) \]

✓ Solution by Mathematica

Time used: 0.786 (sec). Leaf size: 12

DSolve[D[y[x],x]==Exp[x-y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \log \left (e^x+c_1\right ) \]