63.19.2 problem 1(b)

Internal problem ID [13216]
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(b)
Date solved : Tuesday, January 28, 2025 at 05:12:33 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 35

dsolve([diff(x(t),t)=-3*y(t),diff(y(t),t)=-2*x(t)+y(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 74

DSolve[{D[x[t],t]==-3*y[t],D[y[t],t]==-2*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{5} e^{-2 t} \left (c_1 \left (2 e^{5 t}+3\right )-3 c_2 \left (e^{5 t}-1\right )\right ) \\ y(t)\to \frac {1}{5} e^{-2 t} \left (c_2 \left (3 e^{5 t}+2\right )-2 c_1 \left (e^{5 t}-1\right )\right ) \\ \end{align*}