25.1.4 problem 4

Internal problem ID [4216]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 4
Date solved : Monday, January 27, 2025 at 08:42:37 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 0.752 (sec). Leaf size: 12

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

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