Math Is Fun Forum

Old_Steve

Member

Registered: 2007-05-15

Posts: 17

Sum of Power Series to Single Series

I am having trouble reducing the following equation to a single series.  I need to factor out the x variable to solve the diff. eq. by power series method.  I appreciate any help anyone could offer!  I struggle with series stuff. 

The original diff. eq. is

  I used

This latex stuff is nice!

Thanks again!

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: Sum of Power Series to Single Series

Could this help?

---

Numbers are the essence of the Universe

Old_Steve

Member

Registered: 2007-05-15

Posts: 17

Re: Sum of Power Series to Single Series

Thanks but I should be able to substitute the power series into the DE and solve for the coefficeints.

I'm having a hard time solving for the coeff.

I have the following but I'm not sure its right.

This is where I get messed up if I haven't already.  All coeff are supposed to be in terms of

and 

Old_Steve

Member

Registered: 2007-05-15

Posts: 17

Re: Sum of Power Series to Single Series

I guess the goal is to turn the DE into a power series equation, combine the series and solve for the coeff but my Calculus is weak.  Especially in the sereis area.