63.20.1 problem 2(a)

Internal problem ID [13223]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 218
Problem number : 2(a)
Date solved : Tuesday, January 28, 2025 at 05:12:39 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 43

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

\begin{align*} x(t)\to \frac {1}{2} e^{-3 t} \left ((2 c_1+c_2) e^{2 t}-c_2\right ) \\ y(t)\to c_2 e^{-3 t} \\ \end{align*}