65.17.6 problem 30.5 (iii)

Internal problem ID [13847]
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 : 30.5 (iii)
Date solved : Tuesday, January 28, 2025 at 06:05:03 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 32

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

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