Solve the initial value problem

y′′+3y=0

y(0)=1
y′(0)=1

The solution is

Step-by-step explanation:

The question is:

Solve the initial value problem

y′′+3y'=0

y(0)=1

y′(0)=1

Step-by-step explanation:

First, we will write the characteristic equation, which is

Then, we will solve for

becomes

∴ or

or

Hence,

Since the two roots are distinct, that is,

The general solution is

Then,

Then, for

Now, from the question

y(0)=1

y′(0)=1

Then,

Then,

........ (1)

Also,

Then,

....... (2)

∴

From equation (1)

Then,

Hence, and

Then, the solution becomes

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