2. Using Bessel's formula to find solution

x	f(x)
0	135
300	149
600	157
900	183
1200	201
1500	205
1800	193

x = 900

Solution:
Bessel's formula (central difference formula).
The value of table for `x` and `y`

x	0	300	600	900	1200	1500	1800
y	135	149	157	183	201	205	193

Difference table is

x	y	`Deltay`	`Delta^2y`	`Delta^3y`	`Delta^4y`	`Delta^5y`	`Delta^6y`
0	135
		14
300	149		-6
		8		24
600	157		18		-50
		26		-26		70
900	183		-8		20		-86
		18		-6		-16
1200	201		-14		4
		4		-2
1500	205		-16
		-12
1800	193

The value of `x` at you want to find `f(x) : x_0 = 900`

`h = x_1 - x_0 = 300 - 0 = 300`


Bessel's Formula is
`[(dy)/(dx)]_(x=x_0) = 1/h * [Delta y_0 - 1/4 * (Delta^2 y_(0) + Delta^2 y_(-1)) + 1/12 Delta^3 y_(-1) + 1/24 * (Delta^4 y_(-1) + Delta^4 y_(-2)) - 1/120 Delta^5 y_(-2) - 1/120 * (Delta^6 y_(-2) + Delta^6 y_(-3)) + ...]`

`:.[(dy)/(dx)]_(x=900) = 1/300 * [18 - 1/4 * (-14 -8) + 1/12 * (-6) + 1/24 * (4 +20) - 1/120 * (-16) - 1/120 * (0 -86) + ...]`

`:.[(dy)/(dx)]_(x=900) = 1/300 * [18+5.5-0.5+1+0.1333333333+0.7166666667]`

`:.[(dy)/(dx)]_(x=900) = 0.0828`


`[(d^2y)/(dx^2)]_(x=x_0) = 1/h^2 * [1/2 * (Delta^2 y_(0) + Delta^2 y_(-1)) - 1/3 Delta^3 y_(-1) - 1/24 * (Delta^4 y_(-1) + Delta^4 y_(-2)) + 1/24 Delta^5 y_(-2) + 1/180 * (Delta^6 y_(-2) + Delta^6 y_(-3)) + ...]`

`:.[(d^2y)/(dx^2)]_(x=900) = 1/90000 * [1/2 * (-14 -8) - 1/2 * (-6) - 1/24 * (4 +20) + 1/24 * (-16) + 1/180 * (0 -86)]`

`:.[(d^2y)/(dx^2)]_(x=900) = 1/90000 * [-11+3-1-0.6666666667-0.4777777778]`

`:.[(d^2y)/(dx^2)]_(x=900) = -0.0001`