65.17.3 problem 30.1 (iii)

Internal problem ID [13844]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 30, A repeated real eigenvalue. Exercises page 299
Problem number : 30.1 (iii)
Date solved : Tuesday, January 28, 2025 at 06:05:01 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-3 x \left (t \right )-y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )-5 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 30

dsolve([diff(x(t),t)=-3*x(t)-y(t),diff(y(t),t)=x(t)-5*y(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 44

DSolve[{D[x[t],t]==-3*x[t]-y[t],D[y[t],t]==x[t]-5*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

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