67.7.13 problem Problem 6(a)

Internal problem ID [14053]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 8.3 Systems of Linear Differential Equations (Variation of Parameters). Problems page 514
Problem number : Problem 6(a)
Date solved : Monday, March 31, 2025 at 12:01:30 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-3 x \left (t \right )-3 y \left (t \right )+z \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=2 y \left (t \right )+2 z \left (t \right )+29 \,{\mathrm e}^{-t}\\ \frac {d}{d t}z \left (t \right )&=5 x \left (t \right )+y \left (t \right )+z \left (t \right )+39 \,{\mathrm e}^{t} \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 1\\ y \left (0\right ) = 2\\ z \left (0\right ) = 3 \end{align*}

✓ Maple. Time used: 5.552 (sec). Leaf size: 920617

ode:=[diff(x(t),t) = -3*x(t)-3*y(t)+z(t), diff(y(t),t) = 2*y(t)+2*z(t)+29*exp(-t), diff(z(t),t) = 5*x(t)+y(t)+z(t)+39*exp(t)]; 
ic:=x(0) = 1y(0) = 2z(0) = 3; 
dsolve([ode,ic]);
 

\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: 0.088 (sec). Leaf size: 3462

ode={D[x[t],t]==-3*x[t]-3*y[t]+z[t],D[y[t],t]==2*y[t]+2*z[t]+29*Exp[-t],D[z[t],t]==5*x[t]+y[t]+z[t]+39*Exp[t]}; 
ic={x[0]==1,y[0]==2,z[0]==3}; 
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) + 3*y(t) - z(t) + Derivative(x(t), t),0),Eq(-2*y(t) - 2*z(t) + Derivative(y(t), t) - 29*exp(-t),0),Eq(-5*x(t) - y(t) - z(t) - 39*exp(t) + Derivative(z(t), t),0)] 
ics = {x(0): 1, y(0): 2, z(0): 3} 
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
 

OverflowError : mpz too large to convert to float