71.3.19 problem 14

Internal problem ID [14369]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 06:27:54 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: 0.785 (sec). Leaf size: 12

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

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