Differential Equation Power Series Method

lclauber
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Differential Equation Power Series Method (Almost done!)

Homework Statement


solve (2x-1)y'+2y=0 using power series.
I'm really close to the correct answer, which is c/(1-2x). I keep getting 2c/(1-2x).
I got the correct radius of convergence, however (1/2)

Homework Equations


shown in my attempt at a solution.

The Attempt at a Solution


attached as a png.
 

Attachments

  • diffeqproblem7.png
    diffeqproblem7.png
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welcome to pf!

hi lclauberc welcome to pf! :smile:
lclauber said:
I'm really close to the correct answer, which is c/(1-2x). I keep getting 2c/(1-2x).

erm :redface: …

c is arbitrary! :wink:​
 
*facepalm* lol.
Thank you!
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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