60.10.22 problem 1935

Internal problem ID [11933]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1935
Date solved : Monday, January 27, 2025 at 11:47:26 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 )^{2}-z \left (t \right )^{2}\right )\\ \frac {d}{d t}y \left (t \right )&=y \left (t \right ) \left (z \left (t \right )^{2}-x \left (t \right )^{2}\right )\\ \frac {d}{d t}z \left (t \right )&=z \left (t \right ) \left (x \left (t \right )^{2}-y \left (t \right )^{2}\right ) \end{align*}

✗ Solution by Maple

dsolve([diff(x(t),t)=x(t)*(y(t)^2-z(t)^2),diff(y(t),t)=y(t)*(z(t)^2-x(t)^2),diff(z(t),t)=z(t)*(x(t)^2-y(t)^2)],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]^2-z[t]^2),D[y[t],t]==y[t]*(z[t]^2-x[t]^2),D[z[t],t]==z[t]*(x[t]^2-y[t]^2)},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
 

Not solved