y'(x) + x = y(x)

im told y(x)= sum(C_n)(x^n) power series method

i understand how to work the method im just confused about what happens to x?

does it go to 0?does it already have regular a singular point?help,thanks.

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- May 10th 2009, 09:33 AMsheep99quick question, power series method.
y'(x) + x = y(x)

im told y(x)= sum(C_n)(x^n) power series method

i understand how to work the method im just confused about what happens to x?

does it go to 0?does it already have regular a singular point?help,thanks. - May 10th 2009, 10:37 AMCalculus26
See the attachment for the details but the x doesn't magically disappear

but the x term is incorporated into determining the coefficient of the x term once the power series and its derivative are plugged back into the differential equation

You'll notice c1-c0 = 0 considering the contstant term

then 2c2-c1+1 = 0 in considering the linear term this is where x comes in

There are no singularities in this DE - May 10th 2009, 12:28 PMHallsofIvy
This is just y"- y= -x. x= 0 is not a singular point at all!

Let . Then so the equation becomes .

In order to be able to compare "like powers", change the indices. In the first sum, let j= n-2 so that n= j+2. We have

Setting coefficients of like powers equal we have

j= 0:

j= 1:

(**That's**where the "-x" on the right hand side comes in!)

j> 1: