14.4.10 problem 10

Internal problem ID [2528]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.10. Existence-uniqueness theorem. Excercises page 80
Problem number : 10
Date solved : Monday, January 27, 2025 at 05:59:10 AM
CAS classification : [`y=_G(x,y')`]

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

With initial conditions

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved