Idek the answer please help
2 answers:
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Answer:
a) . It does not have a steady state
b) . It has a steady state.
Step-by-step explanation:
a)
The first step is finding . So:
We have to find the eigenvalues of this differential equation, which are the roots of this equation:
So:
Since this differential equation has a positive eigenvalue, it does not have a steady state.
Now as for the particular solution.
Since the differential equation is equaled to a constant, the particular solution is going to have the following format:
So
C is a constant, so (C)' = 0.
The solution in the form is
b)
The first step is finding . So:
We have to find the eigenvalues of this differential equation, which are the roots of this equation:
So:
Since this differential equation does not have a positive eigenvalue, it has a steady state.
Now as for the particular solution.
Since the differential equation is equaled to a constant, the particular solution is going to have the following format:
So
C is a constant, so (C)' = 0.
The solution in the form is
Answer:
4. Slope of function B = -slope of function A
Step-by-step explanation:
Given:
Function A is given as:
The above equation is of the form , where
represents slope of the line.
Therefore, on comparing the function A with the above standard form, er conclude that, slope of function A is -2.
Now, from the graph of function, we consider any two points on the graph and determine the slope of the line using the two points.
Let us consider the points
Now, the slope of the line passing through these two points is given as:
Therefore, slope of function B is 2.
Therefore, the correct relation between the slopes of the two functions is that the slope of function B is negative of the slope of function A.