54.10.20 problem 1935

Internal problem ID [13154]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1935
Date solved : Wednesday, October 01, 2025 at 03:36:44 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right ) \left (y \left (t \right )^{2}-z \left (t \right )^{2}\right )\\ \frac {d}{d t}y \left (t \right )&=y \left (t \right ) \left (z \left (t \right )^{2}-x \left (t \right )^{2}\right )\\ \frac {d}{d t}z \left (t \right )&=z \left (t \right ) \left (x \left (t \right )^{2}-y \left (t \right )^{2}\right ) \end{align*}

✗ Maple

ode:=[diff(x(t),t) = x(t)*(y(t)^2-z(t)^2), diff(y(t),t) = y(t)*(z(t)^2-x(t)^2), diff(z(t),t) = z(t)*(x(t)^2-y(t)^2)]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==x[t]*(y[t]^2-z[t]^2),D[y[t],t]==y[t]*(z[t]^2-x[t]^2),D[z[t],t]==z[t]*(x[t]^2-y[t]^2)}; 
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)**2 + z(t)**2)*x(t) + Derivative(x(t), t),0),Eq((x(t)**2 - z(t)**2)*y(t) + Derivative(y(t), t),0),Eq((-x(t)**2 + y(t)**2)*z(t) + Derivative(z(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t),z(t)],ics=ics)
 

KeyError : F2_