74.4.54 problem 54

Internal problem ID [15947]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 54
Date solved : Tuesday, January 28, 2025 at 08:24:14 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 11

dsolve([diff(y(x),x)=exp(x-y(x)),y(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.723 (sec). Leaf size: 12

DSolve[{D[y[x],x]==Exp[x-y[x]],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \log \left (e^x-1+e\right ) \]