65.15.4 problem 28.2 (iv)

Internal problem ID [13836]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 28, Distinct real eigenvalues. Exercises page 282
Problem number : 28.2 (iv)
Date solved : Tuesday, January 28, 2025 at 06:04:54 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right )+20 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=40 x \left (t \right )-19 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 34

dsolve([diff(x(t),t)=x(t)+20*y(t),diff(y(t),t)=40*x(t)-19*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{-39 t}+c_{2} {\mathrm e}^{21 t} \\ y \left (t \right ) &= -2 c_{1} {\mathrm e}^{-39 t}+c_{2} {\mathrm e}^{21 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 71

DSolve[{D[x[t],t]==x[t]+20*y[t],D[y[t],t]==40*x[t]-19*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{3} e^{-39 t} \left (c_1 \left (2 e^{60 t}+1\right )+c_2 \left (e^{60 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-39 t} \left (2 c_1 \left (e^{60 t}-1\right )+c_2 \left (e^{60 t}+2\right )\right ) \\ \end{align*}