14.1.9 problem 9

Internal problem ID [2480]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 9
Date solved : Monday, January 27, 2025 at 05:53:51 AM
CAS classification : [_separable]

\begin{align*} \sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.125 (sec). Leaf size: 25

dsolve([diff(y(t),t)+sqrt(1+t^2)*exp(-t)*y(t)=0,y(0) = 1],y(t), singsol=all)
 

\[ y = {\mathrm e}^{-\int _{0}^{t}\sqrt {\textit {\_z1}^{2}+1}\, {\mathrm e}^{-\textit {\_z1}}d \textit {\_z1}} \]

✓ Solution by Mathematica

Time used: 0.133 (sec). Leaf size: 32

DSolve[{D[y[t],t]+Sqrt[1+t^2]*Exp[-t]*y[t]==0,{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \exp \left (\int _0^t-e^{-K[1]} \sqrt {K[1]^2+1}dK[1]\right ) \]