- #1
Ratpigeon
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Homework Statement
Find the first five non-zero terms of the power series solution to
d2y/dx2-xy=0 about x=-2; y(-2)=1;y'(-2)=1/2
Homework Equations
... calculus in general?
and the taylor expansion of y(x) is - assuming remainder term is zero:
[itex]\sum[/itex]y(n)(-2)/n! *(x+2)n (n from 0 to infinity)
and y''(x) is:
[itex]\sum[/itex]y(n)(-2)/(n-2)! *(x+2)n-2 (n from 2 to infinity
The Attempt at a Solution
I let x'=x+2, giving:
[itex]\sum[/itex]y(n)(-2)/(n-2)! *(x')n-2-x'[itex]\sum[/itex]y(n)(-2)/n! *(x+2)n +2[itex]\sum[/itex]y(n)(-2)/n! *(x+2)n
(parameters of first sum are from 2 to infinity, of second two sums from 0 to infinity)
But I'm not sure what to do from here - do I need to find y?