60.10.16 problem 1931

Internal problem ID [11851]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1931
Date solved : Sunday, March 30, 2025 at 09:18:30 PM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.871 (sec). Leaf size: 1350

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

\begin{align*} \\ \\ \\ \text {Expression too large to display} \\ \end{align*}

✓ Mathematica. Time used: 2.506 (sec). Leaf size: 1461

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

Timed Out