Maths help (MacLaurin series)

Spitfir3 · 19 Aug 2013 at 18:13

Hey all,

Resit tomorrow and i'm a bit stuck on Q1, part B.

http://img10.imageshack.us/img10/2053/b7q9.jpg

I understand you just differentiate the differential equation and sub in the initial conditions.. but all the examples i've had have had constant coefficients.. the '2x' throws me a bit... but as i've been given y(0) and y'(0) do i just negate that after i've differentiated 2x * y' ?

Cheers

Jonnybmac · 19 Aug 2013 at 18:22

https://www.khanacademy.org/math/ca...taylor/v/cosine-taylor-series-at-0--maclaurin

maybe that can explain?

Spitfir3 · 19 Aug 2013 at 18:26

Jonnybmac said:
https://www.khanacademy.org/math/ca...taylor/v/cosine-taylor-series-at-0--maclaurin

maybe that can explain?

Cheers but the one i'm stuck on involves constructing one from differential equations.

lukeharvest · 19 Aug 2013 at 19:53

Assume a solution exists. Since it exists, it can be uniquely written as a power series. So write y as a generic power series, then substitute it into the differential equation. Combine like terms then use the initial conditions.