50.27.6 problem 6(a)

Internal problem ID [8187]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 10. Systems of First-Order Equations. Section 10.2 Linear Systems. Page 380
Problem number : 6(a)
Date solved : Sunday, March 30, 2025 at 12:47:56 PM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.109 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 57

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

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

✓ Sympy. Time used: 0.052 (sec). Leaf size: 14

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

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