2. Show that the system x ‘ = x – y – x ( x 2 + y 2 ) y ‘ = x + y – y ( x 2 + y 2 ) has a…

2.          Show that the system

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2. Show that the system x ‘ = x – y – x ( x 2 + y 2 ) y ‘ = x + y – y ( x 2 + y 2 ) has a…
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x' = x y x(x2 + y2) y' = x + y y(x2 + y2)

has a periodic solution on the unit circle.