52.10.21 problem 22

Internal problem ID [8415]
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 : 22
Date solved : Sunday, March 30, 2025 at 01:04:20 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=12 x \left (t \right )-9 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=4 x \left (t \right ) \end{align*}

✓ Maple. Time used: 0.116 (sec). Leaf size: 32

ode:=[diff(x(t),t) = 12*x(t)-9*y(t), diff(y(t),t) = 4*x(t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= \frac {{\mathrm e}^{6 t} \left (6 c_2 t +6 c_1 +c_2 \right )}{4} \\ y \left (t \right ) &= {\mathrm e}^{6 t} \left (c_2 t +c_1 \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 46

ode={D[x[t],t]==12*x[t]-9*y[t],D[y[t],t]==4*x[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to e^{6 t} (6 c_1 t-9 c_2 t+c_1) \\ y(t)\to e^{6 t} (4 c_1 t-6 c_2 t+c_2) \\ \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 42

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-12*x(t) + 9*y(t) + Derivative(x(t), t),0),Eq(-4*x(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = 6 C_{1} t e^{6 t} + \left (C_{1} + 6 C_{2}\right ) e^{6 t}, \ y{\left (t \right )} = 4 C_{1} t e^{6 t} + 4 C_{2} e^{6 t}\right ] \]