14.29.1 problem 1

Internal problem ID [2799]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 4. Qualitative theory of differential equations. Section 4.2 (Stability of linear systems). Page 383
Problem number : 1
Date solved : Monday, January 27, 2025 at 06:13:57 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=x \left (t \right )+y\\ y^{\prime }&=-2 x \left (t \right )-2 y \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 26

dsolve([diff(x(t),t)=x(t)+y(t),diff(y(t),t)=-2*x(t)-2*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_1 +c_2 \,{\mathrm e}^{-t} \\ y &= -2 c_2 \,{\mathrm e}^{-t}-c_1 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 58

DSolve[{D[x[t],t]==x[t]+y[t],D[y[t],t]==-2*x[t]-2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{-t} \left (c_1 \left (2 e^t-1\right )+c_2 \left (e^t-1\right )\right ) \\ y(t)\to e^{-t} \left (-2 c_1 \left (e^t-1\right )-c_2 \left (e^t-2\right )\right ) \\ \end{align*}