74.22.3 problem 3

Internal problem ID [16579]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 3
Date solved : Monday, March 31, 2025 at 02:59:32 PM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.110 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 28

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

\begin{align*} x(t)\to c_1 \\ y(t)\to c_2 e^{-2 t} \\ x(t)\to c_1 \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.045 (sec). Leaf size: 12

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

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