Question

For the DE 3 (1 — ӕ)(1 — cos Ta ) 3< а <3 Find and classify the equilibrium points

Answer 1

differential equton Given x) (1- (1- Cos e - 323 For q illibrium t have to We (1-x)(1- cos 1-X 1 1-Co& x = o Ce& TX- CoR X 7 x alutn of form has geven tin Guatin Cos arc Ges (a)+ 21 mi any inges whure Co&n = 1 TxMrCes (1) +27n = Ot 27n where m i 2n belween -3 and lies Heare

To check equidlibium gMth ony quillibrium oid chnging am uncable thedallityofny pait look at We the At ph posithe, then is t is point fomstieto When t moves it isble kide gmph equilliooum, thenermi table at near the maing From ouy At fanix-Aalble Unsta ble at Ride Lamri stole Lode Haus jmph Ami-Atable at ome At 0 1 Jph at me Aern'-table Lede thus At 2= 2 all femi- ble 2 X=0-2

When 20) 2 when 2 2(-1) Y - 2 When 2. 2 (2) 4 Not in onge Trus equilliboim ponte asre 1, 2, -2 qualibaine tgph Now to the sabibty of fest equation y) the gmph boints the ge Have We veagus in Jange 3 sketch We 3. rath of -)(1-(os7x) Tries Vessus X betweey the renge -2 =3