72.9.1 problem 1

Internal problem ID [14718]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Exercises section 3.1. page 258
Problem number : 1
Date solved : Thursday, March 13, 2025 at 04:16:24 AM
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: 0.056 (sec). Leaf size: 20

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 &= 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+1)-c_2 t \\ y(t)\to (c_1-c_2) t+c_2 \\ \end{align*}

✓ Sympy. Time used: 0.058 (sec). Leaf size: 15

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)
 

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