Question

0 dY 5. (6 points) Consider the liner system Y. Determine which of the following dt phase portrait best represents the system. Circle one, or draw a rough sketch to match your choice. Justify your answer.

diff EQ help???

Answer 1

Giren equation is, di 66-7) 7 ti where A = ) and 9+ (%). -6 -7 Then uation o reduces to (2) quation ř = A find Now we from 0 (-:--) 9 Y2 à 92 } (3) Iz - 69, 7% we ý, zo 20 and 42=0 get dizo, 4220 be for fixed point eget, Then from @ so (0,0) is a fixed forint or equilibrium forints of find the edgenvalues and eigenvectors of A. Charmedenstic equation of equation of A is given by well ② and 0 How we Then go to (A) À + det (A) = 0 → ď +7d+6=0 7 dt 6d+n+6=0 de 8+6) +1(8+6)=0 (2+6) (x+1) 20 ~ dal, -6.

for dial we get ☆ di th- 1 (6+) )-(3) 9 (-*-70) - 64) . → 92=-di -6 Y-702= -2 Vi=-12 Take 92=0 Dis-C, C+0 EIR Then vor () for we get, d2 = -6 AY da = > 0 :) -6 -7 9 Y2 o -691 -672 7 72 - 64 - 742 -694 -672 >> Y2 = -67, -691-742 = -692. Take Y=C, 2 =-66,, GEER. Then U2 a (;)

'So, turo are real numbers therefore eegen values of A negative (0,0) fixed point is a stable node. phase diagram Mow . -6 2. 27-1 (-1,1) g slow eigen direction. Here Also from option, and but no option is correct. diagram gives stable node eigen vectors of this diagram diffrent . so, and option is not exactly accurate corresponding froblem 0. So option is correct. are no Note: In this diagram dis- is a tangent of all curves.