60.10.7 problem 1919

Internal problem ID [11918]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1919
Date solved : Monday, January 27, 2025 at 11:47:19 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right )+y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )\\ \frac {d}{d t}y \left (t \right )&=-x \left (t \right )+y \left (t \right )-y \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)-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: 0.000 (sec). Leaf size: 0

DSolve[{D[x[t],t]==x[t]+y[t]-x[t]*(x[t]^2+y[t]^2),D[y[t],t]==-x[t]+y[t]-y[t]*(x[t]^2+y[t]^2)},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Not solved