see the attachment for the questions i am stuck on.
includes first and second order differential equations which need to be solved using Laplace Transforms.
your help would be much appreciated
There is a quick trick to solving for the coefficients of this partial fraction. To find A for example I multiply both sides of the equation by (s+3), now evaluate the left hand side at s = -3 since B is gone.
For A i get (s-3)/(s-1) evaluated at -3 gives 6/4 or 3/2. For B i do the same but multiply both sides by (s-1) and get -1/2
So now take the inverse laplace transform by using a look up table if you wish and I get 1.5e^(-3t) - 0.5e^(-t)
Actually I assumed your previous workings were corrrect but I spotted your denominator is incorrect. Your function in the Laplace domain should be F(s) = (5-s)/[(s-1)(s+3)]. By employing the same procedure as above I seperated the function into its partial fraction components, namely (5-s)/[(s-1)(s+3)] = A/(s-1) + B/(s+3) and found A = 1 and B = -2. The answer I finally got was
F(x) = e^x - 2e^(-3x).
HI I am extremely sorry but I made another small error. The question is very simple its just a small algabraic mistake both me and you have been making.
Notice sX(s) - 1 + 3X(s) = 4/(s-1)
X(s)(s+3) = 4/(s-1) +1
now when you solve for X(s) you should obtain 1/(s-1) becausethe (s+3)'s cancel.
Finally the inverse laplace transfrom of 1/(s-1) is indeed e^t.
Sorry about the previous post, I have been running low on sleep the pastfew days.