# Laplace Transfrom

1. Dec 20, 2011

### okanas

1. The problem statement, all variables and given/known data
could u help to find result? I dont know laplace of u^4(t)??

2. Relevant equations
y''+4y'+5y=3u^4(t)+7(t*u(t)*δ(t-1)

3. The attempt at a solution
The only one i couldn t found is 3u^4(t),,

2. Dec 20, 2011

### I like Serena

Welcome to PF, okanas!

What is the exact definition of u(t)?
If you can say that, can you also say what u4(t) is?

3. Dec 20, 2011

### okanas

thank you Serena,
u4 denoted as a unit step function.

general piecewise (etc u(t-4)f(t-4) ) is easy to solve but power of function itselfs make it undone. Do you have any idea how we can deal with it?

4. Dec 20, 2011

### I like Serena

Huh?

I don't see u(t-4)f(t-4) in your problem statement.

Are we still talking about u4(t)?

5. Dec 20, 2011

### okanas

yes we still talking about u4(t).

u(t) is unit step function.

6. Dec 20, 2011

### vela

Staff Emeritus
Which one is the unit step function, u(t) or u4(t)? Are you using some weird notation you haven't explained to us?

What is this supposed to mean? Please elaborate.

7. Dec 20, 2011

### I like Serena

Okay, so I believe it is defined as:
$$u(t)=\left\{\begin{matrix}0 & \textrm{ if } t < 0 \\ 1 & \textrm{ if } t \ge 0 \end{matrix} \right.$$

What does that mean for u4(t)?

8. Dec 20, 2011

### okanas

That's why i m asking you, what does u4(t) in ODE??
u(t)laplace--->1/s,,right??
So what is laplace u4(t)??

9. Dec 20, 2011

### I like Serena

If you'll bear with me for just a second, please forget about Laplace and the ODE for now.

Do you know what the notation u4(t) means?

Or if you really want the Laplace transform of it, can you give me the definition of the Laplace transform?