Solve Laplace Transform: y''+4y'+5y=3u^4(t)+7(t*u(t)*δ(t-1)

[okanas]

Homework Statement

could u help to find result? I don't know laplace of u^4(t)??

Homework Equations

y''+4y'+5y=3u^4(t)+7(t*u(t)*δ(t-1)

The Attempt at a Solution

The only one i couldn t found is 3u^4(t),,

 

[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?
(Forget about Laplace for now.)

 

[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?

 

[I like Serena]

Huh?

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

Are we still talking about u⁴(t)?

 

[okanas]

yes we still talking about u⁴(t).

u(t) is unit step function.

 

[vela]

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

yes we still talking about u⁴(t).

u(t) is unit step function.

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

general piecewise (etc u(t-4)f(t-4) ) is easy to solve but power of function itselfs make it undone.

What is this supposed to mean? Please elaborate.

 

[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)?

 

[okanas]

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?

forget about this part,,

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)??

 

[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?