54.9.53 problem 1909

Internal problem ID [13131]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 8, system of first order odes
Problem number : 1909
Date solved : Sunday, October 12, 2025 at 02:28:26 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=a x \left (t \right )+g y \left (t \right )+\beta z \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=g x \left (t \right )+b y \left (t \right )+\alpha z \left (t \right )\\ \frac {d}{d t}z \left (t \right )&=\beta x \left (t \right )+\alpha y \left (t \right )+c z \left (t \right ) \end{align*}

✓ Maple. Time used: 10.689 (sec). Leaf size: 31906

ode:=[diff(x(t),t) = a*x(t)+g*y(t)+beta*z(t), diff(y(t),t) = g*x(t)+b*y(t)+alpha*z(t), diff(z(t),t) = beta*x(t)+alpha*y(t)+c*z(t)]; 
dsolve(ode);
 

\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: 0.017 (sec). Leaf size: 1639

ode={D[x[t],t]==a*x[t]+g*y[t]+\[Beta]*z[t],D[y[t],t]==g*x[t]+b*y[t]+\[Alpha]*z[t],D[z[t],t]==\[Beta]*x[t]+\[Alpha]*y[t]+c*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") 
Alpha = symbols("Alpha") 
BETA = symbols("BETA") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
g = symbols("g") 
x = Function("x") 
y = Function("y") 
z = Function("z") 
ode=[Eq(-BETA*z(t) - a*x(t) - g*y(t) + Derivative(x(t), t),0),Eq(-Alpha*z(t) - b*y(t) - g*x(t) + Derivative(y(t), t),0),Eq(-Alpha*y(t) - BETA*x(t) - c*z(t) + Derivative(z(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
 

Timed Out