80.7.14 problem B 6

Internal problem ID [21333]
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 : B 6
Date solved : Thursday, October 02, 2025 at 07:28:30 PM
CAS classification : system_of_ODEs

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

With initial conditions

\begin{align*} x \left (0\right )&=2 \\ y \left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.058 (sec). Leaf size: 24

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 28

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

\begin{align*} x(t)&\to e^t \left (3 e^{2 t}-1\right )\\ y(t)&\to 3 e^{3 t} \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(-x(t) - 2*y(t) + Derivative(x(t), t),0),Eq(-3*y(t) + Derivative(y(t), t),0)] 
ics = {x(0): 2, y(0): 3} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = 3 e^{3 t} - e^{t}, \ y{\left (t \right )} = 3 e^{3 t}\right ] \]