65.17.2 problem 30.1 (ii)

Internal problem ID [13843]
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 (ii)
Date solved : Tuesday, January 28, 2025 at 06:05:00 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-6 x \left (t \right )+2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-2 x \left (t \right )-2 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 32

dsolve([diff(x(t),t)=-6*x(t)+2*y(t),diff(y(t),t)=-2*x(t)-2*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 ) &= \frac {{\mathrm e}^{-4 t} \left (2 c_{2} t +2 c_{1} +c_{2} \right )}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 46

DSolve[{D[x[t],t]==-6*x[t]+2*y[t],D[y[t],t]==-2*x[t]-2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

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