Solve for the function X(s) in the Laplace domain by taking the Laplace transform of the following differential equations with given initial conditions. dx +9x = 161, where x(0) = 0 and (0) = 5

X(s) = 2/[s³(s + 9)]

Step-by-step explanation:

Here is the complete question

Solve for the function X(s) in the Laplace domain by taking the Laplace transform of the following differential equations with given initial conditions.

dx/dt + 9x = 16t²     x(0) = 0 and dx(0)/dt = 5

Solution

dx/dt + 9x = 16t²

Taking the Laplace transform of the differential equation, we have

L{dx/dt + 9x} = L{16t²}

L{dx/dt} + L{9x} = L{16t²}

L{dx/dt} + 9L{x} = 16L{t²}

sL{x} - x(0) + 9L{x}  = 16L{t²}

L{x} = X(s)

L{t²} = 2!/s³

Substituting X(s) and L{t²} into the equation above, we have

sX(s) - x(0) + 9X(s) = 2!/s³

Substituting x(0) = 0 into the equation above, we have

sX(s) - x(0) + 9X(s) = 2!/s³

sX(s) - 0 + 9X(s) = 2!/s³

sX(s) + 9X(s) = 2!/s³

Factorizing X(s), we have

(s + 9)X(s) = 2!/s³

X(s) = 2/[s³(s + 9)]

So X(s) in the Laplace domain is

X(s) = 2/[s³(s + 9)]

x = 12

y = 15

step-by-step explanation:

from the figure we get,

the x axis shows   the months and,

the y-axis shows the number of satisfied customer.

each line or each cell in upward direction (y-axis) shows 500.

the appropriate scale for the y - axis is: -

a = 2000 customers

b = 4000 customers

c = 6000 customers

d = 8000 customers

e = 10000 customers

f = 12000 customers

g = 14000 customers