(a)x=y+x^2+xy^3 (b)x=2x-y+x^2 y=-2x-y^3 y=y(x+1) For (a) I get the critical po

(a)x=y+x^2+xy^3 (b)x=2x-y+x^2 y=-2x-y^3 y=y(x+1) For (a) I get the critical points are(00) and(-2^1/5 4^1/5). Then I get det(00)=2 and det(-2^1/5 4^1/5)=-10 so index of the system is -8 and the index of periodic orbit is 1 so theres no periodic orbit. For (b) I get the critical points are(00)(-1-1)(-20). The det is 2-12 so the index is 3 not equal to 1so no orbit.