# Help needed (Frobenius method)

• Jun 27th 2009, 12:21 PM
razemsoft21
Help needed (Frobenius method)
any 1 can help me on solving the following question plz.

Use Frobenius method to solve the following differential equation

X2Y'' +X(2-X)Y'-2Y= 0
• Jun 30th 2009, 04:50 AM
razemsoft21
just to remember
No answer up tell now , plz. try again
• Jun 30th 2009, 11:14 AM
shawsend
This is how I'd start it and I'm taking this right out of Rainville and Bedient on the chapter on power series solutions:

$\displaystyle 2xy''+x(2-x)y'-2y=0$

Now convert it to the standard form $\displaystyle y''+p(x)y'+q(x)y=0$:

$\displaystyle y''+\frac{x(2-x)}{2x} y'-\frac{1}{x}y=0$

with $\displaystyle p(x)=1-x/2$ and $\displaystyle q(x)=1/x$. That means $\displaystyle p_0=0$ and $\displaystyle q_0=0$ leaving for the indicial equation $\displaystyle c^2-c=0$ giving roots of 0 and 1. So I'd next go to the section dealing with difference of roots a positive integer by first substituting $\displaystyle y(x)=\sum_{n=0}^{\infty} a_n x^{n+c}$ into the original differential equation and continuing.
• Jul 1st 2009, 06:39 AM
shawsend
Razem, I had some problems going further with this as I've been away from it for some time but I do know the route if I had to solve it: Open the book to the first page of that chapter on power series, start reading, do all of the examples, do a few problems in each section, let it simmer over several days, maybe I don't know about 5-10 problems in all. Eventually, I'd get to the point where I could then go back to this problem and work it. That's really in my opinion how to successfully approach a problem you can't solve in math and elsewhere: put it on the back-burner and work some simpler ones first and then "scale-up" :).
• Jul 1st 2009, 12:24 PM
razemsoft21
Quote:

Originally Posted by shawsend
Razem, I had some problems going further with this as I've been away from it for some time but I do know the route if I had to solve it: Open the book to the first page of that chapter on power series, start reading, do all of the examples, do a few problems in each section, let it simmer over several days, maybe I don't know about 5-10 problems in all. Eventually, I'd get to the point where I could then go back to this problem and work it. That's really in my opinion how to successfully approach a problem you can't solve in math and elsewhere: put it on the back-burner and work some simpler ones first and then "scale-up" :).

Thanks for your advice, I am away from this subject for years same as u.
Someone ask me this question, I cann't solve it, and I wont to help him.
Thank you any way.