series solution Watch

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manps
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#1
Report Thread starter 13 years ago
#1
Hi,
need help with this.
find a series solution up to the term x^4 of the D.E

y'' - y' + y = 0

y(0) = 2
y'(0) = 0

thanks
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RichE
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#2
Report 13 years ago
#2
(Original post by manps)
Hi,
need help with this.
find a series solution up to the term x^4 of the D.E

y'' - y' + y = 0

y(0) = 2
y'(0) = 0

thanks

let y(x) = a + bx + cx^2 + dx^3 + ex^4 + ...

So a = 2 and b = 0 from the initial conditions

Putting in the above y into the diff eq we see from the constant/x/x^2 that

2c - b + a = 0
6d - 2c + b = 0
12e - 3d + c =0

solve for c,d,e
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