Question

dy -X dx2 dt =2y-x dt 2. Consider the following system of equations: phase plane, showing only the first quadrant. (a) Graph the nullclines on a (b) Find the fixed points (there are two) to determine the nature of each fixed point (i.e., source, sink, saddle, and (c) Use Jacobian analysis whether it is a node or spiral). (d) Draw the flow arrows in each region of your phase plane from part (a). You may use a computer to help

Answer 1

dt 2Y-X Nu elinus iven by → yニxニ dt 。 dy 2y-x = 0 0 メニ2y メラス Nullcinu on phan plame (only tit quadrant q en by Th finedpoints y(Y-2)0 以ニy→ ニ0

y- 2 +ben =y (4,2),0,0) fined ponts are jacobiam tor the Thu J = 2 Y 2 tined poimt (4,2) foY the Now - 1 1(4/2) -1 iven arre eiqunvaluus -1-> 2- 4 O A-2) (A) 2 = O 2. 2.

Complex oitth poitive insalus one veal Part (4/2) amd et in a un Aable our ee spiral 0,0) poind fire d tor C 3010) - I 2 thin matrix riomgutay 22 eigen valuer an e кeat amd opposite fam. paluus ane a Saddla point eigen vector be the dat tor -1+ 2 - 1 At Y -1 VI

tue eigun pector be vz for 2= C -1 2 2-2 - I Phare plane ait flow ' (0,0) flow Phax plam