Question

Differential Equations power series.

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

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

i need help getting through this problem.. i have worked on it for 5 hours today and i seem to not get the right answer.

Answer 1

I am sorry for not understanding it right away, but you need a power series representation of a family of solutions or Piccardi's method or?

Answer 2

i haven't seen any of that in my text,but it talks about Airy's equation.

http://ltcconline.net/greenl/courses/204/powerlaplace/seriessolutions1.htm

i have found this example online and its similar to my problem but i can seem to get a answer i am satisfied with..

Answer 3

Ok, I will give it a shot then. I think I understand what you need :-)

Answer 4

\[ y = \sum_{0}^{\infty} c _{n} x^n \]

Answer 5

Ok see i have these and this is what you need for these problems.



\[y = \sum_{n=0}^{\infty} A _{n}x ^{n}\]

\[y ' = \sum_{n=1}^{\infty} nA _{n}x ^{n-1}\]

\[y'' = \sum_{n=2}^{\infty}n(n-1)A _{n}x ^{n-2}\]

Answer 6

yes

Answer 7

you plug those in

Answer 8

then set your x power all to the same one

Answer 9

i have these then i need to apply these but where i am getting stuck is when im trying to get my power the same.

Answer 10

I think you can get to this: \[\large 2a_2 - 3a_0 \sum_{n=1}^{\infty}[(n+2)(n+1)a_{n+2} + na_n - 3a_n]x^n = 0\]

Answer 11

so the y' one becomes x^n cause there is an x alreayd there

Answer 12

Typo, there should be a + between the a0 and the sum :-)

Answer 13

From there, I think you have to use the inital condition, though.

Answer 14

nope you use the initial condiditon at the end

Answer 15

you need to plug in values of n

Answer 16

wait are you sure its x(0)=0 and not y(0) = 0?

Answer 17

yes i have reached that far with that same equation.. but i find myself solving a3 a1 and a3 and such.. and thats where im really confused

Answer 18

\[x _{0} =0\]

Answer 19

oh

Answer 20

From there, I think that's the way @eyust707 said, plug in values for n, and try to find a general form for a series representation. But I will leave it to you, guys. I need to go to sleep. I will check back if the problem remains unsolved.

Answer 21

ok thanks man.

Answer 22

No problem. Wasn't too helpful tho :-)

Answer 23

well at least i am not totally off.

Answer 24

I can explain how to solve this but its very difficult to do by typing..

Answer 25

i bet theres a patrickjmt video on almost exactly the same thing

Answer 26

ok on youtube?

Answer 27

http://www.youtube.com/watch?v=6csP7dw0XTY

Answer 28

ok thanks man i will try to figure this out now. and i be back on tomorrow if i need anymore help! thanks much!

Answer 29

if you are cant get it tommorrow and you really want to understand it add me on skype and ill explain it to you. my name is the same on there

Answer 30

ok man i will i cant remember mine right now, but if you get someone random it will probably be me. Thanks

Answer 31

thanks guys i think i got it...