66.1.8 problem Problem 8

Internal problem ID [13855]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 8
Date solved : Tuesday, January 28, 2025 at 06:05:26 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)
 

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

✓ Solution by Mathematica

Time used: 0.757 (sec). Leaf size: 12

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

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