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(a) Show that the system r=x-y- Goty)x, ty - ($12 + y?)y, has at least one closed trajectory. (b) Decide whether or not the ODE

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(a) Show that the system r=x-y- Goty)x, ty - ($12 + y?)y, has at least one closed trajectory. (b) Decide whether or not the ODE i = ety + sin(x), is gradient. It it is, please find a potential. (c) For a ER, consider the differential equation i = (a'+ 2a - 1)Ity, ly = (a+ 1 )a(a - 2)y. For which a e R is the fixed point (0, 0) Liapunov stable? Please explain

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