Laplace transform

1. The problem statement, all variables and given/known data

Find the laplace transform of t sin(t) and t cos(t), and the inverse transform of

2. The attempt at a solution

I found the two laplace forms:



and



I guess I'm supposed to use the two laplace transforms to find the inverse of this one, but I don't know how to do that.

 

hi,

1/(1+s²)² can be written as

1/2[(s²+1-(s²-1))/(s²+1)²]

this can be split as
1/2[(s²+1)/(s²+1)²] - 1/2[(s²-1)/(s²+1)²]

1/2{[1/(s²+1)] - [(s²-1)/(s²+1)²]}

inverse of 1/(s²+1) is sin t and the inverese of next term is (t cost).
Just to bring the denominator in appropriate form we have rearranged as in 1st step.

 

Did you obtain that using separation of variables?

 

just splitting (a - b)/c as a/c - b/c

where
a=s²+1 , b = s² - 1 and c= (s² + 1)².
is this the step you were referring to?

 

Then I'm done with maths for this year. Thanks for helping me with all my problems!