28.4.50 problem 7.50

Internal problem ID [4582]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 7. Systems of linear differential equations. Problems at page 351
Problem number : 7.50
Date solved : Sunday, March 30, 2025 at 03:26:50 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right )-2 x_{3} \left (t \right )+{\mathrm e}^{t}\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=6 x_{1} \left (t \right )-6 x_{2} \left (t \right )+5 x_{3} \left (t \right ) \end{align*}

✓ Maple. Time used: 0.909 (sec). Leaf size: 936

ode:=[diff(x__1(t),t) = -3*x__1(t)+4*x__2(t)-2*x__3(t)+exp(t), diff(x__2(t),t) = x__1(t)+x__2(t), diff(x__3(t),t) = 6*x__1(t)-6*x__2(t)+5*x__3(t)]; 
dsolve(ode);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 1701

ode={D[x1[t],t]==-3*x1[t]+4*x2[t]-2*x3[t]+Exp[t],D[x2[t],t]==x1[t]+x2[t],D[x3[t],t]==6*x1[t]-6*x2[t]+5*x3[t]}; 
ic={}; 
DSolve[{ode,ic},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
t = symbols("t") 
x__1 = Function("x__1") 
x__2 = Function("x__2") 
x__3 = Function("x__3") 
ode=[Eq(3*x__1(t) - 4*x__2(t) + 2*x__3(t) - exp(t) + Derivative(x__1(t), t),0),Eq(-x__1(t) - x__2(t) + Derivative(x__2(t), t),0),Eq(-6*x__1(t) + 6*x__2(t) - 5*x__3(t) + Derivative(x__3(t), t),0)] 
ics = {} 
dsolve(ode,func=[x__1(t),x__2(t),x__3(t)],ics=ics)
 

Timed Out