52.10.18 problem 19

Internal problem ID [8412]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS. EXERCISES 8.2. Page 346
Problem number : 19
Date solved : Wednesday, March 05, 2025 at 05:47:21 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=3 x \left (t \right )-y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=9 x \left (t \right )-3 y \left (t \right ) \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 23

ode:=[diff(x(t),t) = 3*x(t)-y(t), diff(y(t),t) = 9*x(t)-3*y(t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= c_{1} t +c_{2} \\ y &= 3 c_{1} t -c_{1} +3 c_{2} \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 34

ode={D[x[t],t]==3*x[t]-y[t],D[y[t],t]==9*x[t]-3*y[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to 3 c_1 t-c_2 t+c_1 \\ y(t)\to 9 c_1 t-3 c_2 t+c_2 \\ \end{align*}

✓ Sympy. Time used: 0.081 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-3*x(t) + y(t) + Derivative(x(t), t),0),Eq(-9*x(t) + 3*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = 3 C_{1} t + C_{1} + 3 C_{2}, \ y{\left (t \right )} = 9 C_{1} t + 9 C_{2}\right ] \]