- #1
davyyao
- 4
- 0
Hi~
I recently solve a Laplace transform problem as following
L[int{t,0}cosh(t'-1)U(t'-1)dt']=? U(t'-1) is the unit step function(=1 for t'>1, =zero otherwise)
According the standard Laplace formula :
(1)L[cosh(t-1)U(t-1)]=exp(-s)*s/(s^2-1);
(2)L(int{t,0}f(t')dt')=F(s)/s. where F(s)=L(f(t))
I conclude the answer to be:
exp(-s)/(s^2-1)
But from the direct integral formula:
L[int{t,0}cosh(t'-1)U(t'-1)dt']=L[sinh(t-1)]=(1/2)*(exp(-1)/(s-1)-exp(1)/(s+1)).
This two answers are not consistent!
I totally have no idea what's wrong with the two methods?
I believe the second method should be correct by basic definition of Laplace transformation.
Thanks very much!
I recently solve a Laplace transform problem as following
L[int{t,0}cosh(t'-1)U(t'-1)dt']=? U(t'-1) is the unit step function(=1 for t'>1, =zero otherwise)
According the standard Laplace formula :
(1)L[cosh(t-1)U(t-1)]=exp(-s)*s/(s^2-1);
(2)L(int{t,0}f(t')dt')=F(s)/s. where F(s)=L(f(t))
I conclude the answer to be:
exp(-s)/(s^2-1)
But from the direct integral formula:
L[int{t,0}cosh(t'-1)U(t'-1)dt']=L[sinh(t-1)]=(1/2)*(exp(-1)/(s-1)-exp(1)/(s+1)).
This two answers are not consistent!
I totally have no idea what's wrong with the two methods?
I believe the second method should be correct by basic definition of Laplace transformation.
Thanks very much!