The given equations are :
Let's solve for g in equation (2) :
now, let's plug value of g from equation (3) into equation (1) :
plugging value of b in equation (3) :
since " g " represents ground seats, number of ground seats :
=》396
And " b " represents balcony seat, therefore it is equal to :
=》312
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
