# Frobenius method for hermite's differential equation

• Jul 29th 2012, 04:28 PM
Gemma331
Frobenius method for hermite's differential equation
Hello

I am working on a problem but have found myself stuck and confused as to how t continue...

Thr problem is... Using frobenius mood, seek a solution of Hermite's differential equation
d2y/dx2 -2x dy/dx +2my =0 In the form of a power series

Y(x)= (n=0 n= inf) an xx+r A0 =/= 0

Im new to this and not very good with the notation...

I have then found y(x), y'(x) and y''(x) and substitute them into the differential equation it is then I can't work out how t rearrange and Solve... Please helppp!!!
• Jul 29th 2012, 06:33 PM
HallsofIvy
Re: Frobenius method for hermite's differential equation
First there is a good tutorial for "LaTex" formatting that is used on this board. Just start with "[ tex ]" and end with "[/ tex ]" (without the spaces):Introducing LaTeX Math Typesetting

Please show what you have done. What did you get when you differentiated and put y, y', and y'' into the equation?

(You don't really need the "+r" in the exponent because this not really a Frobenious equation- the leading coefficient is never 0 so it is sufficient to look for a solution of the form $\sum_{n=0}^\infty a_nx^n$)
• Jul 30th 2012, 03:06 AM
Gemma331
Re: Frobenius method for hermite's differential equation
The question is a past exam question from a previous year.. It contains the +r so I'm not sure if I would actually have to include it....

So far I have.....

\sum_{n=0}^\infty (n+r-1) a_nx^(n+r-2) - 2 \sum_{n=0}^\infty (n+r) a_nx^(n+r) +2m \sum_{n=0}^\infty a_nx^(n+r)

But its from this I'm stuck what to do next.....