65.17.4 problem 30.1 (iv)

Internal problem ID [13766]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 30, A repeated real eigenvalue. Exercises page 299
Problem number : 30.1 (iv)
Date solved : Wednesday, March 05, 2025 at 10:15:09 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=13 x \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=13 y \left (t \right ) \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 19

ode:=[diff(x(t),t) = 13*x(t), diff(y(t),t) = 13*y(t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{13 t} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{13 t} \\ \end{align*}

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 65

ode={D[x[t],t]==13*x[t],D[y[t],t]==13*y[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to c_1 e^{13 t} \\ y(t)\to c_2 e^{13 t} \\ x(t)\to c_1 e^{13 t} \\ y(t)\to 0 \\ x(t)\to 0 \\ y(t)\to c_2 e^{13 t} \\ x(t)\to 0 \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.063 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-13*x(t) + Derivative(x(t), t),0),Eq(-13*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = C_{1} e^{13 t}, \ y{\left (t \right )} = C_{2} e^{13 t}\right ] \]