how do i solve this problem

Question

pls i need the solution to the problem

Comments

You haven't shown the problem or defined it clearly.

Answer 1

How do I solve this problem: y’’.x.ln(x) = y’’

Since you have y’’ on both sides, then you can cancel both instances, giving

x.ln(x) = 1

ln(x) = 1/x,

which we can write as

f(x) = ln(x) – 1/x   (=0)

We can now use the Newton-Raphson method to give an iterative solution.

The iterative sequence is,

x_(n+1) = x_n – f(x_n) / f’(x_n)   ------------------------------ (1)

 

Starting value (x_1 = ?)

At x = 1: f(1) = ln(1) – 1/1 = -1

At x = 2: f(2) = ln(2) – ½ = 0.1931

There is a change of sign, so the root occurs between x = 1 and x = 2.

Let x_1 = 1.

 

Now tabulate the calculations

n	x_n	f(x_n)	f’(x_n)	x_(n+1) using (1)
1	1	-1	2	1.5
2	1.5	-0.2612	1.1111	1.73508
3	1.73508	-0.02528	0.9085	1.76292
4	1.76292	-2.7328x10^(-4)	0.8891	1.76322
5	1.78322	-3.2446x10^(-8)	0.8888	1.76322

 

Solution: x = 1.76322