74.4.48 problem 48

Internal problem ID [15941]
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 : 48
Date solved : Tuesday, January 28, 2025 at 08:23:58 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 5

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

\[ y = t \]

✓ Solution by Mathematica

Time used: 0.771 (sec). Leaf size: 9

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

\[ y(t)\to \log \left (e^t\right ) \]