63.19.6 problem 1(f)

Internal problem ID [13141]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 202
Problem number : 1(f)
Date solved : Wednesday, March 05, 2025 at 09:18:08 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-6 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=6 y \left (t \right ) \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 22

ode:=[diff(x(t),t) = -6*y(t), diff(y(t),t) = 6*y(t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= -c_{2} {\mathrm e}^{6 t}+c_{1} \\ y &= c_{2} {\mathrm e}^{6 t} \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 30

ode={D[x[t],t]==-6*y[t],D[y[t],t]==6*y[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to -c_2 e^{6 t}+c_1+c_2 \\ y(t)\to c_2 e^{6 t} \\ \end{align*}

✓ Sympy. Time used: 0.062 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(6*y(t) + Derivative(x(t), t),0),Eq(-6*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = C_{1} - C_{2} e^{6 t}, \ y{\left (t \right )} = C_{2} e^{6 t}\right ] \]