Solve these linear equations in the form y=yn+yp with yn=y(0)e^at.
a. y'-4y=-8
b. y'+4y=8
which one has a steady state?

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

81 seats

step-by-step explanation:

if you multiply 0.65 times 125 then you get 81.5 seats. well since you can't have half of a seat you have to round down and get 81 seats in the no children zones. that leave 44 seats outside of the no children zone.

d

step-by-step explanation: