Question

(s^2 - 4s + 4) I need help to solve partial fractions in

Answer 1

First factor it.

Answer 2

It's complex roots are.
s=2-6i
s=2+6i

Answer 3

Where is the fraction?

Answer 4

@marielen123 you have to have a fraction to partial it. yours is not a fraction, what should we do ?

Answer 5

I would like to solve partial fraction, using the formula

Answer 6

but s^2 -4s + 4 = (s^2 -2) ^2 no get to result

Answer 7

yes, one moment

Answer 8

y'' - 4y' + 4y = 3 δ ( t - 1) + δ ( t-2) it is the question

Answer 9

laplace, because solving the question

Answer 10

y(s) =[ 3e^-s + e^-2s + s -3] / s^2 -4s + 4

Answer 11

in this site, I know many many mathematicians who are experts this problem, let me tag them @Psymon @wio @UsukiDoll

Answer 12

ok, thank you

Answer 13

@marielen123 when using Laplace, we need initial value, what are they?

Answer 14

I tag others but I still work by myself. If I got it, I will show you

Answer 15

the initial values it is y(0) = 1 and y'(0) = 1 @Loser66

Answer 16

First factor the denominator.

Answer 17

@marielen123 got you
@wio I need work from the beginning by myself, what if she makes mistake at somewhere?

Answer 18

@marielen123 I don't think you have to use partial fraction there, from the laplace table, you have formula #13 which talks about \(e^{-cs}F(s)\) your F(s) is \(\dfrac{1}{s^2-4s+4}\)
just by that way, you can figure out the inverse of that Laplace

Answer 19

for the last 2 parts, s/ wholething, , you have to apply formula #16 . only the last one, which is 3/ wholething you can manipulate to get the form of formula #11(this is the easiest one)
I don't see any thing else can apply to your case. I am sorry.

Answer 20

I think apply formula #10

Answer 21

he is not here, but when he came online, you can tag him. I am pretty sure that he is willing to help and his major is Math. he is @SithandGiggle
I apply #10 and got stuck, since yours is 4s when it needs 6s for the complete square.

Answer 22

ok, apply: [(s-2) -1] / (s-2) ^2

Answer 23

I understand, thank you

Answer 24

hehe ok

Answer 25

I am very good at poking others. heehe.. good luck, I have a bunch of homework to do.

Answer 26

ahaaha... you are right at the post above, you are sooooo smart

Answer 27

hehe, thank you

Answer 28

flattering you first, poking you later. wait there. girl