( ) Power series solution for ODE

[Deathcrush]

(URGENT) Power series solution for ODE

Homework Statement

Supose there is an infinite series solution$$\sum b_{n}x^{n}$$ for

u''+4(x-(1/4))^2*u+C(x) = 0 where C(x) is a function (I get it in another problem, I'll put it in the relevant equations area), determinate the coefitients $$b_{0} b_{1} b_{2} b_{3} b_{4}$$and express an approximate solution, use C to express the whole function in terms of r

Homework Equations

u''+4(x-(1/4))^2*u+C(x) = 0 the ODE

C(x)=(.3(e^r)(1-e^r)/r)
I am also given some initial conditions, but I don't think they are relevant for now

The Attempt at a Solution

I derived the proposed solution and used it in the ODE, then I changed the indexes and took some terms out of the sum so that I would get only one series, after that, I am supposed to get a relationship between the b's so that I can get those b's , but I don't seem to find it, since there are too many terms out of the sum. Any idea? this should be done for tomorrow :S

 

[mighty2000]

Hello,

Thank you for posting your question on the forum. I understand that you are working on finding the coefficients for the infinite series solution for the ODE u''+4(x-(1/4))^2*u+C(x) = 0, and you are having trouble finding the relationship between the coefficients b's. I would recommend taking a closer look at the terms that you have taken out of the sum and see if you can simplify them further. It is possible that there may be a common factor that can be factored out, which would make it easier to find the relationship between the coefficients. Additionally, you could try substituting the series solution back into the ODE and see if you can manipulate it to get a relationship between the coefficients. I hope this helps. Good luck with your assignment!