52.9.8 problem 8

Internal problem ID [8386]
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 : 8
Date solved : Sunday, March 30, 2025 at 12:56:46 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=7 x \left (t \right )+5 y \left (t \right )-9 z \left (t \right )-8 \,{\mathrm e}^{-2 t}\\ \frac {d}{d t}y \left (t \right )&=4 x \left (t \right )+y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{5 t}\\ \frac {d}{d t}z \left (t \right )&=-2 y \left (t \right )+3 z \left (t \right )+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \end{align*}

✓ Maple. Time used: 5.411 (sec). Leaf size: 8567

ode:=[diff(x(t),t) = 7*x(t)+5*y(t)-9*z(t)-8*exp(-2*t), diff(y(t),t) = 4*x(t)+y(t)+z(t)+2*exp(5*t), diff(z(t),t) = -2*y(t)+3*z(t)+exp(5*t)-3*exp(-2*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: 0.202 (sec). Leaf size: 3002

ode={D[x[t],t]==7*x[t]+5*y[t]-9*z[t]-8*Exp[-2*t],D[y[t],t]==4*x[t]+y[t]+z[t]+2*Exp[5*t],D[z[t],t]==-2*y[t]+3*z[t]+Exp[5*t]-3*Exp[-2*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(-7*x(t) - 5*y(t) + 9*z(t) + Derivative(x(t), t) + 8*exp(-2*t),0),Eq(-4*x(t) - y(t) - z(t) - 2*exp(5*t) + Derivative(y(t), t),0),Eq(2*y(t) - 3*z(t) - exp(5*t) + Derivative(z(t), t) + 3*exp(-2*t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
 

Timed Out