use the methods of frobenius to solve

**compufatwa** · October 26th 2007, 08:16 AM

use the methods of frobenius to solve:

2xy"+y'+2y =0

i want to know not just the answer but the steps how to answer it (explanation of the answer)

**ThePerfectHacker** · October 26th 2007, 09:35 AM

Originally Posted by compufatwa

use the methods of frobenius to solve:

2xy"+y'+2y =0

i want to know not just the answer but the steps how to answer it (explanation of the answer)

The charachteristic equation is,
$2r(r-1) + r+0=0$ thus, $r=0,1/2$ .
This means to look for solutions of the form:
$y=\sum_{n=0}^{\infty} a_n x^n$ and $y=\sum_{n=0}^{\infty} a_n x^{n+1/2}$
Can you take it from there?

**compufatwa** · October 26th 2007, 01:00 PM

ur point of view is not clear to me can u tell me more info about it

**ThePerfectHacker** · October 27th 2007, 03:22 PM

Originally Posted by compufatwa

ur point of view is not clear to me can u tell me more info about it

Given the equation,
$x^2p(x)y''+xq(x)y'+r(x)y=0$
Where $p(x),q(x),r(x)$ are analytic functions* on some open interval $(-R,R)$ .
The method of Frobenius says that we can look for a solution of the form,
$y=\sum_{n=0}^{\infty}a_n x^{n+r}$ for some number $r$ .
Now to find this $r$ we solve the equation,
$r(r-1)p(0) + rq(0) + r(0) = 0$ .
So I told you what $r$ has to be.

*)"Analytic" on $(-R,R)$ means the function can be expanded as its Taylor series about any point, in this case about 0.

Yes, I got a question about Islam. Did you know that Halos (the floating circles around your head) were created by Christians. If so why would you use them?

**compufatwa** · October 28th 2007, 01:05 PM

i do not think that the question is about islam ,but it's about the floating circles around icon head, it's just an icon i know that it's used in the art as in church and many famous art drawing .

Thread: use the methods of frobenius to solve

LinkBack

Thread Tools

Display

use the methods of frobenius to solve

Similar Math Help Forum Discussions

easy methods to solve percentage problems

dw/dt how to solve by two methods

[SOLVED] Use graphical methods to solve a linear programming problem

Numerical methods to solve higher order differential equations

Using numerical methods to solve problems

Search Tags