- #1
ChemistryNat
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Homework Statement
Let y(x)=[itex]\sum[/itex]ckxk (k=0 to ∞) be a power series solution of
(x2-1)y''+x3y'+y=2x, y(0)=1, y'(0)=0
Note that x=0 is an ordinary point.
Homework Equations
y(x)=[itex]\sum[/itex]ckxk (k=0 to ∞)
y'(x)=[itex]\sum[/itex](kckxk-1) (k=1 to ∞)
y''(x)=[itex]\sum[/itex](k(k-1))ckxk-2 (k=2 to ∞)
The Attempt at a Solution
(x2-1)[itex]\sum[/itex](k(k-1))ckxk-2 (k=2 to ∞) +[itex]\sum[/itex](kckxk) (k=1 to ∞)+[itex]\sum[/itex]ckxk (k=0 to ∞) -2x=0 ??
I'm not having an issue with the power series themselves, I'm just not sure how to incorporate in the "2x" term when I'm setting up the series equation. We didn't cover this scenario in class and I couldn't find anything like it in my textbook.
I've been trying to incorporate it as a series itself
ie. 2[itex]\sum[/itex]ckxk (k=0 to ∞) where C0=0, or 2[itex]\sum[/itex]ckxk (k=1 to ∞)
but I'm not sure I can even do that mathematically?Thank you!