Internal problem ID [10241]
Internal file name [OUTPUT/9188_Monday_June_06_2022_01_36_48_PM_22714112/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1919.
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 )&=-x \left (t \right ) y \left (t \right )^{2}-x \left (t \right )^{3}+y \left (t \right )+x \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )^{2} y \left (t \right )-y \left (t \right )^{3}-x \left (t \right )+y \left (t \right ) \end {align*}
Does not currently support non linear system of equations. This is the phase plot of the system.
✗ Solution by Maple
dsolve([diff(x(t),t)=x(t)+y(t)-x(t)*(x(t)^2+y(t)^2),diff(y(t),t)=-x(t)+y(t)-y(t)*(x(t)^2+y(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]-x[t]*(x[t]^2+y[t]^2),y'[t]==-x[t]+y[t]-y[t]*(x[t]^2+y[t]^2)},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Not solved