65.15.1 problem 28.2 (i)

Internal problem ID [13833]
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 (i)
Date solved : Tuesday, January 28, 2025 at 06:04:52 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=8 x \left (t \right )+14 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=7 x \left (t \right )+y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 35

dsolve([diff(x(t),t)=8*x(t)+14*y(t),diff(y(t),t)=7*x(t)+y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{15 t}+c_{2} {\mathrm e}^{-6 t} \\ y \left (t \right ) &= \frac {c_{1} {\mathrm e}^{15 t}}{2}-c_{2} {\mathrm e}^{-6 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 71

DSolve[{D[x[t],t]==8*x[t]+14*y[t],D[y[t],t]==7*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{3} e^{-6 t} \left (c_1 \left (2 e^{21 t}+1\right )+2 c_2 \left (e^{21 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-6 t} \left (c_1 \left (e^{21 t}-1\right )+c_2 \left (e^{21 t}+2\right )\right ) \\ \end{align*}