Thread: Power series solution

Hi guys,

May I confirm if my approach is correct so far as I work towards the solution.

I apologize in advance, it looks a bit long, but it is just the first few steps of the approach (no work on equating coefficients etc yet)

1) This ODE has a regular singular point at x=0 and so Frobenius Method is used where
?

2) If 1) is correct, when I try to write it out as a series I obtain 3 series:

Which simplifies to:


May I confirm if this is correct?

3) My next question is that I attempt to make the summation indexes the same - i.e. n=5. However I get a large number of terms that need to be taken out of the first 2 series - so wanted to confirm if my approach is correct in the first place.

Thank you for any feedback given
Linda

2) is correct.
3) Let n=N-4 and rewrite the last sum, starting from N=4. After, the character "N" can be replaced by the character "n".
For information : The EDO is one of Bessel kind. Solutions are :
y = C1 x^(3/2) BesselJ[1/2 , x^3] +C2 x^(3/2) BesselJ[-1/2 , x^3]

Hi JJacquelin,

Thank you for taking the time to look at it and confirm my approach.

I have let n=N-4 and the series solution works out.
May I just confirm if the solution should be:
?

Thank you!!!