52.10.17 problem 16

Internal problem ID [8411]
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 8.2. Page 346
Problem number : 16
Date solved : Sunday, March 30, 2025 at 01:02:35 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )+2 x_{3} \left (t \right )-\frac {9 x_{4} \left (t \right )}{5}\\ \frac {d}{d t}x_{2} \left (t \right )&=\frac {51 x_{2} \left (t \right )}{10}-x_{4} \left (t \right )+3 x_{5} \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )\\ \frac {d}{d t}x_{4} \left (t \right )&=x_{2} \left (t \right )-\frac {31 x_{3} \left (t \right )}{10}+4 x_{4} \left (t \right )\\ \frac {d}{d t}x_{5} \left (t \right )&=-\frac {14 x_{1} \left (t \right )}{5}+\frac {3 x_{4} \left (t \right )}{2}-x_{5} \left (t \right ) \end{align*}

✓ Maple. Time used: 0.270 (sec). Leaf size: 1388

ode:=[diff(x__1(t),t) = x__1(t)+2*x__3(t)-9/5*x__4(t), diff(x__2(t),t) = 51/10*x__2(t)-x__4(t)+3*x__5(t), diff(x__3(t),t) = x__1(t)+2*x__2(t)-3*x__3(t), diff(x__4(t),t) = x__2(t)-31/10*x__3(t)+4*x__4(t), diff(x__5(t),t) = -14/5*x__1(t)+3/2*x__4(t)-x__5(t)]; 
dsolve(ode);
 

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

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 2839

ode={D[ x1[t],t]==x1[t]+2*x3[t]-18/10*x4[t],D[ x2[t],t]==51/10*x2[t]-x4[t]+3*x5[t],D[ x3[t],t]==x1[t]+2*x2[t]-3*x3[t],D[ x4[t],t]==x2[t]-31/10*x3[t]+4*x4[t],D[ x5[t],t]==-28/10*x1[t]+15/10*x4[t]-x5[t]}; 
ic={}; 
DSolve[{ode,ic},{x1[t],x2[t],x3[t],x4[t],x5[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") 
x__4 = Function("x__4") 
x__5 = Function("x__5") 
ode=[Eq(-x__1(t) - 2*x__3(t) + 9*x__4(t)/5 + Derivative(x__1(t), t),0),Eq(-51*x__2(t)/10 + x__4(t) - 3*x__5(t) + Derivative(x__2(t), t),0),Eq(-x__1(t) - 2*x__2(t) + 3*x__3(t) + Derivative(x__3(t), t),0),Eq(-x__2(t) + 31*x__3(t)/10 - 4*x__4(t) + Derivative(x__4(t), t),0),Eq(14*x__1(t)/5 - 3*x__4(t)/2 + x__5(t) + Derivative(x__5(t), t),0)] 
ics = {} 
dsolve(ode,func=[x__1(t),x__2(t),x__3(t),x__4(t),x__5(t)],ics=ics)
 

MatrixError : Jordan normal form is not implemented if the matrix have eigenvalues in CRootOf form