87.20.2 problem 2

Internal problem ID [23687]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 3. Linear Systems. Exercise at page 161
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:44:16 PM
CAS classification : system_of_ODEs

\begin{align*} x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right ) \end{align*}

✓ Maple. Time used: 0.043 (sec). Leaf size: 30

ode:=[diff(x__1(t),t) = 3*x__1(t)-2*x__2(t), diff(x__2(t),t) = x__1(t)]; 
dsolve(ode);
 

\begin{align*} x_{1} \left (t \right ) &= 2 c_1 \,{\mathrm e}^{2 t}+c_2 \,{\mathrm e}^{t} \\ x_{2} \left (t \right ) &= c_1 \,{\mathrm e}^{2 t}+c_2 \,{\mathrm e}^{t} \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 54

ode={D[x1[t],t]==3*x1[t]-2*x2[t],D[x2[t],t]==x1[t]}; 
ic={}; 
DSolve[{ode,ic},{x1[t],x2[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} \text {x1}(t)&\to e^t \left (c_1 \left (2 e^t-1\right )-2 c_2 \left (e^t-1\right )\right )\\ \text {x2}(t)&\to e^t \left (c_1 \left (e^t-1\right )-c_2 \left (e^t-2\right )\right ) \end{align*}

✓ Sympy. Time used: 0.072 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
x1 = Function("x1") 
x2 = Function("x2") 
ode=[Eq(-3*x1(t) + 2*x2(t) + Derivative(x1(t), t),0),Eq(-x1(t) + Derivative(x2(t), t),0)] 
ics = {} 
dsolve(ode,func=[x1(t),x2(t)],ics=ics)
 

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