Question

please answer the following questions. Please show all work and write your answers neatly and thoroughly please. Thank you.

2. Consider the one-parameter family of ordinary differential equations ay = y2 – 3y+a. Locate the bifurcation value of a and sketch the phase line for a value of a below, equal to, and above a

Answer 1

of May ta a=o => dolat=0 Y-3y + o=0 y = 0,3l equilibria asl doldt=0 LV-34 tao 3 I 19-400 Yo si v equilibrio asa , dl dt = 0 y² - 3y + 220 y za 24 -Y +250 ' Y (Y-2) 1 (Y-1) = 0 Y=12 asrl, dx/dt =0 y? – 37-10 Y = 31 19 + 4 ly = 3 I VB l equilibnja

for a-q we get Y -34+9=0 4 y-3 50 Y-3 -Seguiliboi XOX Z 13-55 a-ra fata o al a 2 Noequilibria parabola Bifurcation diagram