Question

Please help with step-by-step notes for the laplace transform: y'' +6y'+5y = 12e^t

Answer 1

initial conditions??

Answer 2

sorry, y(0) = -1 y'(0) = 7

Answer 3

do you know the laplace of dy/dt?

Answer 4

F(s)?

Answer 5

L(dy/dt) = sL(y)-y(0)

Answer 6

oh, that formula. yes. i usually can get to the partial fractions part, but I usually have trouble separating the terms and whatnot

Answer 7

L(d^2y/dt^2) = s^2L(y)-y`(0) - sy(0)

Answer 8

well show me what you got when you get to the partial fractions part

Answer 9

Y(s) = (12 -s+13)/((s-1)(s^2 +6s+5))

Answer 10

and that is where i am confused

Answer 11

....and that's wrong...

Answer 12

now i have Y(s) = (-s^2 + 14s -13) / ((s-1)(s^2 +6s +5))

Answer 13

1 sec

Answer 14

thank you

Answer 15

let me know if you need more help

Answer 16

thank you

Answer 17

np

Answer 18

oh snap. matrices?

Answer 19

yeah do u know them?

Answer 20

you can do the same thing just solving three equations with three unknowns, its just longer.

Answer 21

are you getting it?