74.22.8 problem 8

Internal problem ID [16655]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 09:16:18 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=8 x-y \left (t \right )\\ y^{\prime }\left (t \right )&=x+6 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.045 (sec). Leaf size: 30

dsolve([diff(x(t),t)=8*x(t)-y(t),diff(y(t),t)=x(t)+6*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{7 t} \left (c_{2} t +c_{1} \right ) \\ y &= {\mathrm e}^{7 t} \left (c_{2} t +c_{1} -c_{2} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 44

DSolve[{D[x[t],t]==8*x[t]-y[t],D[y[t],t]==x[t]+6*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{7 t} (c_1 (t+1)-c_2 t) \\ y(t)\to e^{7 t} ((c_1-c_2) t+c_2) \\ \end{align*}