Internal problem ID [10227]
Internal file name [OUTPUT/9174_Monday_June_06_2022_01_34_18_PM_58677329/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1905.
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 )&=h \left (t \right ) y \left (t \right )-g \left (t \right ) z \left (t \right )\\ y^{\prime }\left (t \right )&=f \left (t \right ) z \left (t \right )-h \left (t \right ) x \left (t \right )\\ z^{\prime }\left (t \right )&=x \left (t \right ) g \left (t \right )-y \left (t \right ) f \left (t \right ) \end {align*}
Does not currently support non autonomous system of first order linear differential equations. The following is the phase plot
✗ Solution by Maple
dsolve([diff(x(t),t)=h(t)*y(t)-g(t)*z(t),diff(y(t),t)=f(t)*z(t)-h(t)*x(t),diff(z(t),t)=g(t)*x(t)-f(t)*y(t)],singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x'[t]==h[t]*y[t]-g[t]*z[t],y'[t]==f[t]*z[t]-h[t]*x[t],z'[t]==g[t]*x[t]-f[t]*y[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
Not solved