78.5.5 problem 2.d

Internal problem ID [21044]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 6, Linear systems. Problems section 6.9
Problem number : 2.d
Date solved : Thursday, October 02, 2025 at 07:01:43 PM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.141 (sec). Leaf size: 20

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

\begin{align*} x \left (t \right ) &= \left (-c_2 t +c_1 \right ) {\mathrm e}^{t} \\ y \left (t \right ) &= c_2 \,{\mathrm e}^{t} \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 26

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

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

✓ Sympy. Time used: 0.037 (sec). Leaf size: 22

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

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