65.15.1 problem 28.2 (i)

Internal problem ID [13754]
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 : Wednesday, March 05, 2025 at 10:14:57 PM
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*}

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

ode:=[diff(x(t),t) = 8*x(t)+14*y(t), diff(y(t),t) = 7*x(t)+y(t)]; 
dsolve(ode);
 

\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*}

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

ode={D[x[t],t]==8*x[t]+14*y[t],D[y[t],t]==7*x[t]+y[t]}; 
ic={}; 
DSolve[{ode,ic},{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*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-8*x(t) - 14*y(t) + Derivative(x(t), t),0),Eq(-7*x(t) - y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = - C_{1} e^{- 6 t} + 2 C_{2} e^{15 t}, \ y{\left (t \right )} = C_{1} e^{- 6 t} + C_{2} e^{15 t}\right ] \]