Solve by means of Laplace transforms

[chrisking2021]

1. Please see attachment for Question I've put it into microsoft eqn editor.


2. I have not got a clue where to begin i don't want anyone to do it for me but some information on how i can do it for myself would be appreciated.


3. as above

 

[Defennder]

Here is the question for those who don't want to risk infection or are lazy to download and open:
y''+6y'+13y = 0, y(0) = 3, y'(0) = 7.


Well, you start by applying the Laplace transform to both the LHS and RHS. What is Laplace transform of y'', y' ? Express it in terms of L(y) and then throw all the other terms to the RHS, and find the inverse Laplace transform of RHS. Then plug in the initial value conditions.