52.9.6 problem 6

Internal problem ID [8384]
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 8.1. Page 332
Problem number : 6
Date solved : Sunday, March 30, 2025 at 12:53:56 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-3 x \left (t \right )+4 y \left (t \right )+{\mathrm e}^{-t} \sin \left (2 t \right )\\ \frac {d}{d t}y \left (t \right )&=5 x \left (t \right )+9 z \left (t \right )+4 \,{\mathrm e}^{-t} \cos \left (2 t \right )\\ \frac {d}{d t}z \left (t \right )&=y \left (t \right )+6 z \left (t \right )-{\mathrm e}^{-t} \end{align*}

✓ Maple. Time used: 6.141 (sec). Leaf size: 6670

ode:=[diff(x(t),t) = -3*x(t)+4*y(t)+exp(-t)*sin(2*t), diff(y(t),t) = 5*x(t)+9*z(t)+4*exp(-t)*cos(2*t), diff(z(t),t) = y(t)+6*z(t)-exp(-t)]; 
dsolve(ode);
 

\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✓ Mathematica. Time used: 0.534 (sec). Leaf size: 2949

ode={D[x[t],t]==-3*x[t]+4*y[t]+Exp[-t]*Sin[2*t],D[y[t],t]==5*x[t]+9*z[t]+4*Exp[-t]*Cos[2*t],D[z[t],t]==y[t]+6*z[t]-Exp[-t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t],z[t]},t,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
z = Function("z") 
ode=[Eq(3*x(t) - 4*y(t) + Derivative(x(t), t) - exp(-t)*sin(2*t),0),Eq(-5*x(t) - 9*z(t) + Derivative(y(t), t) - 4*exp(-t)*cos(2*t),0),Eq(-y(t) - 6*z(t) + Derivative(z(t), t) + exp(-t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
 

Timed Out