65.15.5 problem 28.6 (iii)

Internal problem ID [13837]
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 : 28.6 (iii)
Date solved : Tuesday, January 28, 2025 at 06:04:55 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-2 x \left (t \right )+2 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: 24

dsolve([diff(x(t),t)=-2*x(t)+2*y(t),diff(y(t),t)=x(t)-y(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 71

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

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