S.O.S. Mathematics CyberBoard

[John Williams]

Obtain terms to ORDER 3
using series solution for sin(y) gives:

Series solution will be of the form:

Then

Then substituting for y and y' in the ode:
I finally arrive at, after equating coefficients of like powers of x:



After finally expressing all the a's in terms of a_0 and using the fact that

I get a completely different answer to the BOOK ANSWER which is:

[aswoods]

I get the same result as you...

[John Williams]

Hi Aswoods
Just to be clear, what do you get your final answer as?
John

[outermeasure]

[John Williams]

Hi Outermeasure
You mean
Expansion of siny about pi/2:
..?
John

[outermeasure]

[John Williams]

Oops. Of Course!
Thanks
John

[John Williams]

Hi again
I must admit this one is still causing me problems.
My working is:

On expanding and equating like powers of x and thus deriving expressions for all the a's in terms of a_0, and using a_0=y(0)=pi/2
I do not get the book answer.
BOOK ANSWER IS:

John

[outermeasure]

[John Williams]

Hi Outermeasure
I have now obtained the correct answer by the method of SUCCESSIVE DIFFERENTIATIONS but I'm dammed if I can get it by the method of UNDETERMINED COEFFICIENTS!
Sorry about this but I'm going to need some spoon feeding on getting it by this method.
Regards
John

[outermeasure]

[John Williams]

Thanks Outermeasure
Quite easy really.
I must be getting old!
John