Internal problem ID [5734]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-{\mathrm e}^{x -y}=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.743 (sec). Leaf size: 12
DSolve[y'[x]==Exp[x-y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \log \left (e^x+c_1\right ) \]