7.23.1 problem 1

Internal problem ID [587]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 5. Linear systems of differential equations. Section 5.2 (Applications). Problems at page 345
Problem number : 1
Date solved : Tuesday, March 04, 2025 at 11:27:16 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-x \left (t \right )+3 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=2 y \left (t \right ) \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 26

ode:=[diff(x(t),t) = -x(t)+3*y(t), diff(y(t),t) = 2*y(t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= c_2 \,{\mathrm e}^{2 t}+{\mathrm e}^{-t} c_1 \\ y \left (t \right ) &= c_2 \,{\mathrm e}^{2 t} \\ \end{align*}

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 35

ode={D[x[t],t]==-x[t]+3*y[t],D[y[t],t]==2*y[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to e^{-t} \left (c_2 \left (e^{3 t}-1\right )+c_1\right ) \\ y(t)\to c_2 e^{2 t} \\ \end{align*}

✓ Sympy. Time used: 0.084 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(x(t) - 3*y(t) + Derivative(x(t), t),0),Eq(-2*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

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