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 most boring ever written

step-by-step explanation:

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