65.17.1 problem 30.1 (i)

Internal problem ID [13842]
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 (i)
Date solved : Tuesday, January 28, 2025 at 06:04:59 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=5 x \left (t \right )-4 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: 0.036 (sec). Leaf size: 34

dsolve([diff(x(t),t)=5*x(t)-4*y(t),diff(y(t),t)=x(t)+y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= \frac {{\mathrm e}^{3 t} \left (2 c_{2} t +2 c_{1} -c_{2} \right )}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 45

DSolve[{D[x[t],t]==5*x[t]-4*y[t],D[y[t],t]==x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{3 t} (2 c_1 t-4 c_2 t+c_1) \\ y(t)\to e^{3 t} ((c_1-2 c_2) t+c_2) \\ \end{align*}