60.10.17 problem 1932

Internal problem ID [11852]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1932
Date solved : Sunday, March 30, 2025 at 09:18:31 PM
CAS classification : system_of_ODEs

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==x[t]*(y[t]-z[t]),D[y[t],t]==y[t]*(z[t]-x[t]),D[z[t],t]==z[t]*(x[t]-y[t])}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t],z[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
z = Function("z") 
ode=[Eq((-y(t) + z(t))*x(t) + Derivative(x(t), t),0),Eq((x(t) - z(t))*y(t) + Derivative(y(t), t),0),Eq((-x(t) + y(t))*z(t) + Derivative(z(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
 

KeyError : F2_