60.9.50 problem 1905

Internal problem ID [11904]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 8, system of first order odes
Problem number : 1905
Date solved : Monday, January 27, 2025 at 11:44:22 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=h \left (t \right ) y \left (t \right )-g \left (t \right ) z \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=f \left (t \right ) z \left (t \right )-h \left (t \right ) x \left (t \right )\\ \frac {d}{d t}z \left (t \right )&=x \left (t \right ) g \left (t \right )-y \left (t \right ) f \left (t \right ) \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[{D[x[t],t]==h[t]*y[t]-g[t]*z[t],D[y[t],t]==f[t]*z[t]-h[t]*x[t],D[z[t],t]==g[t]*x[t]-f[t]*y[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
 

Not solved