Find all critical points of the given plane autonomous system. (Enter your answers as a comma-separated list.) x′ = x 12 − x − 1 2 y y′ = y(20 − y − x)

Answer:

the critical points are (0,0) , (0, 20), (12, 0) , (4,16)

Step-by-step explanation:

To consider the autonomous system

[tex]x' =x (12 -x - \dfrac{1}{2})[/tex]

[tex]y' = y( 20 -y - x)[/tex]

The critical points of the above system can be derived by replacing x' = o and y' = 0.

i.e.

[tex]x' =x (12 -x - \dfrac{y}{2}) = 0[/tex]

[tex]\dfrac{x}{2} (24 -2x - y) = 0[/tex]

x = 0 or 24 - 2x - y = 0     ----- (1)

Also

[tex]y' = y( 20-y-x) = 0[/tex]

y( 20 -y - x) = 0

y = 0 or 20 - y - x = 0  -----   (2)

By solving (1) and (2);

we get x = 4 and y = 16

Suppose x = 0 from (2)

y = 20

Also;

if y = 0 from (1)

x = 12

Thus, the critical points are (0,0) , (0, 20), (12, 0) , (4,16)

HELP PLEASE.............

Zelda rode her bike at a steady rate of 12 miles per hour for 3

please help UwU
also hope your day is going GREAT >w

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