52.9.9 problem 9

Internal problem ID [8387]
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 : 9
Date solved : Sunday, March 30, 2025 at 12:57:20 PM
CAS classification : system_of_ODEs

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.185 (sec). Leaf size: 3251

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

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✗ Sympy

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

Timed Out