Solving a convolution equation: two solutions, which one is correct?
Here is my problem:
Considering the following equation,
- Ur(t) is what we are looking for and is =0 for all t<0
- * is a convolution
- G(t) = 1/Q1 + (P1/Q2-1/Q1)exp(-Q1.t/Q2) for t>=0 (Q1, Q2 and P1 are constants) and G(t)=0 for all t<0
- A is a constant
I derived a solution using the Laplace Transform and also found a way to get a solution through a derivation in the time domain using the Stieltjes integrals . Both derivations are in the .doc attached
The issue is that the two solutions are different and I don't know why...
Which one is correct if any?(Wondering)
Thanks for your help or ideas,