85.92.3 problem 1 (c)

Internal problem ID [23052]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 11. Matrix eigenvalue methods for systems of linear differential equations. A Exercises at page 528
Problem number : 1 (c)
Date solved : Thursday, October 02, 2025 at 09:18:21 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )-2 x \left (t \right )+3 y \left (t \right )&=0\\ -2 x \left (t \right )+\frac {d}{d t}y \left (t \right )+3 y \left (t \right )&=0 \end{align*}

✓ Maple. Time used: 0.049 (sec). Leaf size: 25

ode:=[diff(x(t),t)-2*x(t)+3*y(t) = 0, diff(y(t),t)-2*x(t)+3*y(t) = 0]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= c_1 +c_2 \,{\mathrm e}^{-t} \\ y \left (t \right ) &= c_2 \,{\mathrm e}^{-t}+\frac {2 c_1}{3} \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 60

ode={D[x[t],{t,1}]-2*x[t]+3*y[t]==0, D[y[t],{t,1}]-2*x[t]+3*y[t]==0}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.042 (sec). Leaf size: 20

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

\[ \left [ x{\left (t \right )} = \frac {3 C_{1}}{2} + C_{2} e^{- t}, \ y{\left (t \right )} = C_{1} + C_{2} e^{- t}\right ] \]