Answer:
Step-by-step explanation:
Given that,
y' = 17y ( 1-y^7)
Let y=1
Then, y' = 0 for all t
Then show that it is the only stable equilibrium point so that as y→1, t→∞ with any initial value.
So, the graph solution will be
y(0) = 1 and this will be an horizontal line
If, y(0) > 1 then, y' < 0 by inspecting the first equation, so the graph is has decreasing solution.
Likewise, if y(0) < 1 then, y' > 0 and the graph is increasing.
So no matter the initial condition, graph of the solution will be asymptotic to the horizontal line above.
This make the limit be 1.
This shows that x = 1 is a stable equilibrium.
a) Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of equations
b) since the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of equation
In order to show if the given point corresponds to the given function, we will have to substitute the value of x into the function to see if we will have its corresponding y-value
For the point (-0.8, -0.6), substitute x = -0.8 into both functions as shown:
f(x) = 2x + 1
f(-0.8) = 2(-0.8) + 1
f(-0.8) = -1.6 + 1
f(-0.8) = -0.6
Simiarly;
y = -3(-0.8)- 3
y = 2.4 - 3
y = -0.6
Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of equations
For the point (1/3, 2), substitute x = 1/3 into both functions as shown:
x = (y+2)/2
x = (2+2)/2
x = 4/2
x = 2
Simiarly;
x + 2 = 3
x = 3-2
x = 1
Since the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of equations
Learn more on systems of equation here: brainly.com/question/847634
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Step-by-step explanation:
