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Am I missing something in the Frobenius method??
Use the method of Frobenius to find solutions near x= 0 of each of the differential equations.
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.
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.
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