Internal problem ID [9516]
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 }\relax (t )&=-x \relax (t ) y \relax (t )^{2}+x \relax (t )+y \relax (t )\\ y^{\prime }\relax (t )&=x \relax (t )^{2} y \relax (t )-x \relax (t )-y \relax (t )\\ z^{\prime }\relax (t )&=y \relax (t )^{2}-x \relax (t )^{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},{x(t), y(t), z(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]^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