52.10.16 problem 15

Internal problem ID [8410]
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 : 15
Date solved : Sunday, March 30, 2025 at 01:01:03 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=\frac {9 x \left (t \right )}{10}+\frac {21 y \left (t \right )}{10}+\frac {16 z \left (t \right )}{5}\\ \frac {d}{d t}y \left (t \right )&=\frac {7 x \left (t \right )}{10}+\frac {13 y \left (t \right )}{2}+\frac {21 z \left (t \right )}{5}\\ \frac {d}{d t}z \left (t \right )&=\frac {11 x \left (t \right )}{10}+\frac {17 y \left (t \right )}{10}+\frac {17 z \left (t \right )}{5} \end{align*}

✓ Maple. Time used: 0.227 (sec). Leaf size: 918

ode:=[diff(x(t),t) = 9/10*x(t)+21/10*y(t)+16/5*z(t), diff(y(t),t) = 7/10*x(t)+13/2*y(t)+21/5*z(t), diff(z(t),t) = 11/10*x(t)+17/10*y(t)+17/5*z(t)]; 
dsolve(ode);
 

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 616

ode={D[x[t],t]==9/10*x[t]+21/10*y[t]+32/10*z[t],D[y[t],t]==7/10*x[t]+65/10*y[t]+42/10*z[t],D[z[t],t]==11/10*x[t]+17/10*y[t]+34/10*z[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t],z[t]},t,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
z = Function("z") 
ode=[Eq(-9*x(t)/10 - 21*y(t)/10 - 16*z(t)/5 + Derivative(x(t), t),0),Eq(-7*x(t)/10 - 13*y(t)/2 - 21*z(t)/5 + Derivative(y(t), t),0),Eq(-11*x(t)/10 - 17*y(t)/10 - 17*z(t)/5 + Derivative(z(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
 

Timed Out