Laplace transformation question

[sfgoat]

Trying to answer the question:
x"+3x'+2x=u(t-1)+2(t-2)u(t-2), x(0)=1, x'(0)=-1

My book has the answer but I need to see how to solve a problem like this. Professor didn't have time to cover this section but he said one of these might be on the test. Any help is greatly appreciated.

 

[SteamKing]

Paul's Online Math Notes has a pretty good introduction to Laplace Transforms (and so should the text used in your DE course):

http://tutorial.math.lamar.edu/Classes/DE/LaplaceIntro.aspx

There are some lecture videos here:

https://www.physicsforums.com/threads/ordinary-differential-equations.110274/

Check out Post #10 at the link above. There are 3 or 4 videos which show how to use LTs to solve ODEs for various forcing functions.

Unfortunately, PF is not set up to be a tutoring service, so after studying the material, if you have any questions, please feel free to post any follow ups.