Internal problem ID [10259]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1937.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right ) y \left (t \right )^{2}+x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )^{2} y \left (t \right )-x \left (t \right )-y \left (t \right )\\ z^{\prime }\left (t \right )&=y \left (t \right )^{2}-x \left (t \right )^{2} \end {align*}
✗ Solution by Maple
dsolve([diff(x(t),t)=-x(t)*y(t)^2+x(t)+y(t),diff(y(t),t)=x(t)^2*y(t)-x(t)-y(t),diff(z(t),t)=y(t)^2-x(t)^2],singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x'[t]==-x[t]*y[t]^2+x[t]+y[t],y'[t]==x[t]^2*y[t]-x[t]-y[t],z'[t]==y[t]^2-x[t]^2},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
Not solved