Question

please be clear and prefer to type the solution. please draw the same sample I post it

3.(25pm) Cimder fhe automunious first-onder DE = + -12 )Find the equililibum slutions int: first, completely factor the RHS of the DE Draw the phase lime and dlassify cach equilibrium solution as a repeller, attractor, or semi-stable. By ndssitraight edge), sketch the graph ofa typical solution yi) when ( 3(0)=2 (iv) (0)=4 (a) = -2 (c) If is a solution of the IVP +-12y.0) e, evaluate the following: iy lim yt ( 1 (vani-st ウェー1 ( tor) at うt -1 additional Frsletim yo)-2 at Fin d lim 914) モー20

Answer 1

DE s gIven as 94+y3 1292 3 (a) Facler of R4S : t+ y3_12y2= y2( 4) ( 9-3) 92(9+4) (9-3 olt giveo by Eqyi cbruim point' It is y2(yt4) (4-3)= o y-3 9I-4 phase-Line dy = g+(9+4) (y-3) dt for dt ter -4<4<o , dy トo at for 9-4 at for at is saddle p010h (semi stable tlearly crihcal po int y0 is a Repell er y= 3 a thractor an y=-4 is ( TYPIcal soluhon for y(o= -5 -4 ylo)-5 (り yの= ー2 y(o)-2. -4 y (0) 2 Ja-4 yio)= 4 Hs 9t)-9 y 31 yc trapob

dyyt3ny re) yit 910)= e2 7 t y(y+4) (y-3) dt y-3 Frem graph 七→ー。 YO)= e = 2.7 t+o 1es awith o443 curve Hence Lim Yi 3 tzo ゴニー4 Lim yft)

Hope it helps you out.

In case any doubt please feel free to ask.

I will be happy to help you.

Thanks!!