Differential equation first example in class

: Math 2730 Sequences and Series: Differential equation first example in class
   By Anonymous on Tuesday, April 22, 2008 - 02:45 pm: Edit Post

Hi! When going through the examples you did in class on differential equations, I came across a question:

For the first example: y'-y=0 , expanding the power series representation of this you get:
n=0: c1=c0
n=1: c2= 1/2 c0
n=2: C3= 1/2*1/3* c0

but then your expression for Cn is:

Cn= 1/n! * C0

why is it not Cn= 1/(n+1)! * C0 ???


   By Sasho on Tuesday, April 22, 2008 - 05:13 pm: Edit Post

Because the index in Cn is related to C0 via the formula Cn=1/n! C0. It is the over-usage of n that confused you. Perhaps it might hep if you use, say m, and write: Cm=1/m! C0.


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