Internal problem ID [2546]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{x -y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 9
dsolve(diff(y(x),x)=exp(x-y(x)),y(x), singsol=all)
\[ y \relax (x ) = \ln \left ({\mathrm e}^{x}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.281 (sec). Leaf size: 12
DSolve[y'[x]==Exp[x-y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (e^x+c_1\right ) \\ \end{align*}