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...
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.
\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 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...