60.10.19 problem 1932

Internal problem ID [11930]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1932
Date solved : Monday, January 27, 2025 at 11:47:24 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*}

✗ Solution by Maple

dsolve([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))],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{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])},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
 

Not solved