80.7.36 problem D 5

Internal problem ID [21355]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 7. System of first order equations. Excercise 7.6 at page 162
Problem number : D 5
Date solved : Thursday, October 02, 2025 at 07:28:43 PM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.049 (sec). Leaf size: 31

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

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 59

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

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

✓ Sympy. Time used: 0.079 (sec). Leaf size: 31

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

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