Find an autonomous differential equation with all of the following properties: equilibrium solutions at y=0 and y=3,
y' > 0 for 0 y' < 0 for -inf < y < 0 and 3 < y < inf
dy/dx =

dy/dt = y ( 3 - y )

Step-by-step explanation:

Given data:

Determine an autonomous differential equation with the following properties

y = 0 and Y = 3

y' > 0 for  0 < y < 3

y' < 0 for  -∞ < y < 0  and  3 < y < ∞

considering an autonomous differential equation

dy/dt = y ( 3 - y )

y = 0 and 3 represents equilibrium solutions

if 0 < y < 3  then y ( 3 - y ) > 0  for   0 < y < 3

hence : dy / dt = y' > 0  for 0 < y < 3

y ( 3 - y ) <  0  for -∞ < y < 0 and  3 < y < ∞

hence : dy / dt = y' < 0  for  -∞ < y < 0  and  3 < y < ∞

this shows that the autonomous differential equation satisfies every condition hence the autonomous differential equation is :

dy/dt = y ( 3 - y )

the answer is 11.2 (i know i’m late)

hello, sorry being so rude after all that fighting i found it kind of funny, so as me saying sorry here is an answer!

since the table showed her that   2km = 2000m.

to determine, how many km in 2000m, she would divide by 1000.

= 2000 / 1000 = 2 km.

similarly, for 8000m = 8000 / 1000 = 8 km

cheers to savings

~

your pal papaguy