Question

what is the laplace transform of y? is it sy(s) or sy(0)? or maybe y(s) or y(0)?

..i think s is just used for derivatives...im so confused

Answer 1

@waterineyes i would appreciate a quick help

Answer 2

I have one http://www.math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/ode/laplace/lt/lt.html

Answer 3

so y would be...?

Answer 4

one sec

Answer 5

either it's not there...or there's too many things written that i cant see it

Answer 6

no according the website y is 0 that is the answer I saw as I was scrolling on the website

Answer 7

if you want me to I will copy and past this answer for you.

Answer 8

lol what o.O

Answer 9

here is the break down


Translation Property

The translation formula states that Y(s) is the Laplace transform of y(t), then



where a is a constant. Here is an example. The Laplace transform of the
y(t)=t is Y(s)=1/s^2. Hence



Laplace Transform of the Derivative

Suppose that the Laplace transform of y(t) is Y(s). Then the Laplace
Transform of y'(t) is



For the second derivative we have



For the n'th derivative we have



Derivatives of the Laplace Transform

Let Y(s) be the Laplace Transform of y(t). Then

Answer 10

Laplace transform of y means:

\(\mathcal{L}(y)\)..

Answer 11

^that doesnt answer my question :|

Answer 12

@godorovg i dont get what you said

Answer 13

It's like a parametrization of the function y(t) into y(s).

Answer 14

can everyone stop beating around the bush....it's just a simple question o.O

Answer 15

im asking if the laplace of y is y(s), y(0), sy(s) or sy(0)

Answer 16

im doubting it's the s ones...i think the s ones are used in y'

Answer 17

maybe i should just post the original question...

Answer 18

\[y^\prime + y = e^{2t}; \; y(0) = 0\]
i know y' = sy(s) - y(0)

my problem is y

Answer 19

so what's the laplace of y?

Answer 20

Yes I got it @lgbasallote