Recent content by th3chemist

Homework Statement The question is y' - xy = 0 I have to solve it using series solutions Homework Equations The Attempt at a Solution I use y = Ʃ from 0 to infinity a_n x^n and took the derivative. I plugged it into the equation I got the recurrence relation to be a1 = 0...

Like if I start at n=1, I plug that number in and get that an*x or w/e. Then I can rewrite the series to start at n=2.

Can't I get all of them to start at n=2 if I remove some terms from it?

sigh :( I thought you're supposed to turn the whole thing into one series. Then determine a_n+2

But those don't start at the same n. How can you find the recurrence relation then? :(

Oh! It's x = 1, sorry.

It's my 4th one that I cannot seem to shift down. Like it starts at n=0. so the smallest value it starts with is x. Thought I pressume I will have to rip that function out. But I don't know :(. I used k=n-1 , k = n-2 , k = n-1 , k = n+1 and the last one is fine on it's own.

I'm not sure how you multiplied x * (x-1) with each other :(

\sum n(n+1)(a_{n})(x-1)^{n-1} + \sum n(n+1)(a_{n})(x-1)^{n-2} + \sum (n)(a_{n})(x-1)^{n-1} + \sum a_{n}(x-1)^{n+1} + \sum a_{n}(x-1)^{n} that looks about right. Idk how to put the n = at the bottom. But their upper limit is infinity.For the first two, n = 2, the middle one is n=1, and the...

I'm not sure how to use latex :(

I have no clue what I'm doing anymore. To add series together they have to have the same exponent on x and the n value also has to be the same. But I can't seem to get that. I know I have to so I can get the recurrence relation. And the question asks to find the first four terms.

Homework Statement I have to solve the differential equation xy'' + y' + xy = 0 ; x_o = 0 Homework Equations The Attempt at a Solution I know that a solution is y= sum from 0 to infinity (an (x-1)^n) I then differentiate it twice to get y' = sum from 1 to inifinity...

So my answer is wrong? :(

I just don't see it :(. And the limit for -n/(n+1) = -1. As you divide n by the top and bottom. So the answer should be e^-1?

1/n^2 = -n^-2 though. Oh wait I think I see it now. What can I do after I have -n/(n+1)? I can't take the limit yet. It would be ∞/∞