63.19.4 problem 1(d)

Internal problem ID [13218]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 202
Problem number : 1(d)
Date solved : Tuesday, January 28, 2025 at 05:12:34 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=-2 x-y \left (t \right )\\ y^{\prime }\left (t \right )&=-4 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 27

dsolve([diff(x(t),t)=-2*x(t)-y(t),diff(y(t),t)=-4*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= \frac {c_{2} {\mathrm e}^{-4 t}}{2}+c_{1} {\mathrm e}^{-2 t} \\ y &= c_{2} {\mathrm e}^{-4 t} \\ \end{align*}

✓ Solution by Mathematica

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

DSolve[{D[x[t],t]==-2*x[t]-y[t],D[y[t],t]==-4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{2} e^{-4 t} \left ((2 c_1-c_2) e^{2 t}+c_2\right ) \\ y(t)\to c_2 e^{-4 t} \\ \end{align*}