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Theorem 2. Let E be an open subset of R² and suppose that fe C(E). Let y(t) be a periodic solution of (1) of period T. Then4. Show that the system • = -y + (1 – 22 - y2)2 y = 1+ y(1 - x? - y2)2 has a limit cycle r represented by y(t) = (cost, sin t

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az -Y+x (1-2 yg ý z txty (1-2 Myny put no neuso, Yassimo now ona xå ry ý za [ + x (1-2%*)] ay [x+y (12] z amen) (1-2 ) = mikoif cao, then nyl, and on astro Agar cayo we see that roll a nyl as ta. This shows that there exist a single closed path Good

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