Question

Differential Equations power series.

y''+xy'-3y=0 x_(0) = 0

obtain up to the 13th term of the power series...

I just need some help getting started and understanding which formulas to use.

Answer 1

u have to define y to be a sum...
then you plug and make the index of summations start at the same place in order to get a general sol'n and just work out the pattern for what the thirteenth term will be

Answer 2

ok i have this but dont know how to apply this.

\[y= \sum_{k=0}^{\infty} A _{k}z ^{k}\]

\[y \prime = \sum_{k=0}^{\infty} k A _{k}z ^{k-1}\]

\[y \prime \prime = \sum_{k=0}^{\infty} k(k-1)A _{k}z ^{k-2}\]

Answer 3

can you tell me what these terms are? like A and k ? i think z is like my x

Answer 4

these terms are used to plug in for all the y's...

Answer 5

and yes z is x

Answer 6

yep i understand that but what about k? is k what term i want?

Answer 7

k will be plugged in when the 13th term comes around...treat k as a variable when simplifying

Answer 8

so am i working my way up to the 13th term? i'm so confused

Answer 9

plug in all the sums to ur equation, then simplify and get an overall expression after plugging in initial conditions...and then using the patterns found u can get the 13th term

Answer 10

is this kinda like the maclaurin series?

Answer 11

no, youre plugging in sums to the eqn to simplify and get a general solution in terms of a power series

Answer 12

ok thanks Q i'll try to work this out