60.10.18 problem 1933

Internal problem ID [11853]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1933
Date solved : Sunday, March 30, 2025 at 09:18:32 PM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 1.215 (sec). Leaf size: 4317

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

\begin{align*} \left [\left \{x \left (t \right ) &= \frac {2}{2 c_2 -t}\right \}, \left \{y \left (t \right ) = \left (\int -\frac {x \left (t \right )^{2} {\mathrm e}^{-\int x \left (t \right )d t}}{2}d t +c_1 \right ) {\mathrm e}^{\int x \left (t \right )d t}\right \}, \{z \left (t \right ) = x \left (t \right )\}\right ] \\ \left [\left \{x \left (t \right ) &= \frac {2}{2 c_2 -t}\right \}, \{y \left (t \right ) = x \left (t \right )\}, \left \{z \left (t \right ) = \left (\int -\frac {x \left (t \right )^{2} {\mathrm e}^{-\int x \left (t \right )d t}}{2}d t +c_1 \right ) {\mathrm e}^{\int x \left (t \right )d t}\right \}\right ] \\ \text {Expression too large to display} \\ \end{align*}

✗ Mathematica

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

AttributeError : list object has no attribute func