Thread: Help with laplace tranforms question...

1. Help with laplace tranforms question...

Here is the problem:
Use laplace transforms to solve
IVP

How do I solve this? Should I do 2 separate equations or is there a theorem I use? Please help me get a few steps to get started.

2. Originally Posted by isu2014
Here is the problem:
Use laplace transforms to solve
IVP

How do I solve this? Should I do 2 separate equations or is there a theorem I use? Please help me get a few steps to get started.
Two seperate functions. Let $\displaystyle LT[y(t)] = Y(s)$ and $\displaystyle LT[x(t)] = X(s)$ and solve simultaneously for Y and X. Then invert each etc.

3. Originally Posted by mr fantastic
Two seperate functions. Let $\displaystyle LT[y(t)] = Y(s)$ and $\displaystyle LT[x(t)] = X(s)$ and solve simultaneously for Y and X. Then invert each etc.
Thanks, now I'm confused because I've only dealt with y', x' not y'', x''. How do I make equations with the double primes?

4. See here for a table that will show you the Laplace Transforms of second derivatives (and higher).

5. Now I have:
$\displaystyle (s^2+4)Y(s) + 3X(s) = 0$
$\displaystyle (s^2+1)X(s) + 4Y(s) = 0$

Determinate: $\displaystyle -(s^4 - 5s^2 + 8)$

Is this correct? And what next?

6. Originally Posted by isu2014
Now I have:
$\displaystyle (s^2+4)Y(s) + 3X(s) = 0$
$\displaystyle (s^2+1)X(s) + 4Y(s) = 0$

Mr F says: The above equations are not correct.

Determinate: $\displaystyle -(s^4 - 5s^2 + 8)$

Is this correct? And what next?
You have not correctly applied the formula for the Laplace transform of the double derivative of x and y. You need to go back and do this more carefully.

Once you have the correct equations, you have to solve them simultaneously to get X and Y in terms of s. Then you have to get the inverse Laplace transform of each.