Solving Frobenius Method Problems: Tips & Tricks

[Heat]

Am I missing something in the Frobenius method??

Homework Statement

Use the method of Frobenius to find solutions near x= 0 of each of the differential equations.

The Attempt at a Solution

x^2 y'' + (2x^2 + 3x)y' + (x-(5/4))y = 0

My work is as follows:

http://imgur.com/3XvP4.jpg

I don't know where I went wrong, or what I'm doing wrong. My r's are correct of 1/2 and -5/2.

I use r =1/2 first, and when I evaluate for n = 1 I get...

..x^1/2 [c_o - c_o/2 x + c_o/5 x^2 + 2c_o /5 + ...]


the answer in the back of the book has the last line in that pic. I know that I haven't finished solving for the other r, but the portion that is circles with the arrow, does not match what I have so far. I noticed they have their sigma starting at n=0. I tried evaluating them for the n's but my answer differ. :(

please help.

 

[gabbagabbahey]

I know that I haven't finished solving for the other r, but the portion that is circles with the arrow, does not match what I have so far. I noticed they have their sigma starting at n=0. I tried evaluating them for the n's but my answer differ. :(

please help.

There's your problem. Remember, the r=-5/2 series will also have terms of order x^1/2, x^3/2, etc. When you add the terms of these orders from both your r=1/2 and r=-5/2 series together, you should get the right answer.

 

[Heat]

I'll go ahead and do that, will post back.

Thanks gabba.