Internal problem ID [10253]
Internal file name [OUTPUT/9201_Monday_June_06_2022_01_43_13_PM_40877412/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1932.
ODE order: 1.
ODE degree: 1.
The type(s) of ODE detected by this program : "system of linear ODEs" Unable to solve or complete the solution.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right ) y \left (t \right )-x \left (t \right ) z \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right ) y \left (t \right )+y \left (t \right ) z \left (t \right )\\ z^{\prime }\left (t \right )&=x \left (t \right ) z \left (t \right )-y \left (t \right ) z \left (t \right ) \end {align*}
Does not currently support non linear system of first order linear differential equations.
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[{x'[t]==x[t]*(y[t]-z[t]),y'[t]==y[t]*(z[t]-x[t]),z'[t]==z[t]*(x[t]-y[t])},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
Not solved