The given equation is
1. Find two linearly independent solutions of the form . Using the recurrence relation.
I changed the given y to
Then I found the first and second derivatives.
When I plug it in back into the original equation, I get:
+ + -
Ok, I understand up to this part. Now I'm just confused after this, but this is what I got. I took out
+ + -
Then I tried to get and changed some of the n values to and similar to what my professor did.
Then I tried to find the r by:
I got r = 1/2 and r = -1.
Is this correct so far? When my professor went over a homework question similar to this problem, he said that the r's would be -1 and -1/2. I just don't see where the -1/2 came from and even so. When I plug -1 , I get zero in the third term which ruins it unless that's ok?
I know what to do pass this part, but it's very confusing. I spent more than 5 hours trying to do this and I know I'm doing something wrong or thinking of something else. Please help me lead to the right direction.
Well, I believe I already got the indicial equation. It's near the end of the post, just in terms of r. First part of that long function.
I got and .
Then I plug in the r values and set up all the functions . I did this for each r value and when r = -1, the third term is zero and ruins it and can't get the fourth non-zero term.
Maybe I'm looking at this a different way?
Did I make a sign error or something?