63.21.1 problem 1(a)

Internal problem ID [13229]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 225
Problem number : 1(a)
Date solved : Tuesday, January 28, 2025 at 05:12:45 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=-3 x+y \left (t \right )\\ y^{\prime }\left (t \right )&=-3 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 23

dsolve([diff(x(t),t)=-3*x(t)+y(t),diff(y(t),t)=-3*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= \left (c_{2} t +c_{1} \right ) {\mathrm e}^{-3 t} \\ y &= {\mathrm e}^{-3 t} c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

DSolve[{D[x[t],t]==-3*x[t]+y[t],D[y[t],t]==-3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{-3 t} (c_2 t+c_1) \\ y(t)\to c_2 e^{-3 t} \\ \end{align*}