1. ## manipulating series

ok, so i am working on power series solutions to differential equations and need to get some things straight. after substituting into the in question differential equation the required power series derivatives, say there is an X^2 coefficient and i need to bring it inside one of the series; should the starting point for that series be decreased by two (because the power on X outside the series is 2 and is being added to the X^[n+s] term to make it X^[n+s+2])?

also, how do i type in formulas is there perchance a program to do this?

2. Originally Posted by mobius2000
ok, so i am working on power series solutions to differential equations and need to get some things straight. after substituting into the in question differential equation the required power series derivatives, say there is an X^2 coefficient and i need to bring it inside one of the series; should the starting point for that series be decreased by two (because the power on X outside the series is 2 and is being added to the X^[n+s] term to make it X^[n+s+2])?

also, how do i type in formulas is there perchance a program to do this?
First for La Tex use the math tages

use the $\Sigma$

button for math tags. Here is a link to La Tex code. There is a place to practice and with some basic code on this site.n You can also put your mouse above others code (or double click on it) to see others code

http://en.wikipedia.org/wiki/Help Formula

I think you mean this

$y=\sum_{n=0}^{\infty}c_nx^n$

$y'=\sum_{n=1}^{\infty}c_nnx^{n-1}$

$y'-xy=0 \iff \sum_{n=0}^{\infty}c_nx^n -x\sum_{n=1}^{\infty}c_nnx^{n-1}$

$\sum_{n=0}^{\infty}c_nx^n -\sum_{n=1}^{\infty}c_nnx^{n}=c_0+\sum_{n=1}^{\inft y}c_nx^n -\sum_{n=1}^{\infty}c_nnx^{n}=c_0+ \sum_{n=1}^{\infty}\left( c_n-c_nn\right)x^n$

I hope this helps.