54.10.21 problem 1936

Internal problem ID [13155]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1936
Date solved : Sunday, October 12, 2025 at 02:35:49 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. Time used: 1.026 (sec). Leaf size: 700

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);
 

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

✗ 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_