87.21.3 problem 3

Internal problem ID [23717]
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 178
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:44:33 PM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.044 (sec). Leaf size: 30

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 42

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

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

✓ Sympy. Time used: 0.073 (sec). Leaf size: 36

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

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