65.17.6 problem 30.5 (iii)

Internal problem ID [13768]
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 : 30.5 (iii)
Date solved : Wednesday, March 05, 2025 at 10:15:11 PM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.034 (sec). Leaf size: 18

ode:=[diff(x(t),t) = -x(t)+y(t), diff(y(t),t) = -x(t)+y(t)]; 
dsolve(ode);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 32

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

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

✓ Sympy. Time used: 0.060 (sec). Leaf size: 17

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

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