Dirac delta function under integral?

  • Thread starter chempinaki
  • Start date
  • #1
Hello all,
I joined this amazing forum just today.I hope that my question will get answered soon.
So here it is.I am unable to understand a some steps in calculation. Please help me understand.

Here is a linear homogeneous first order differential equation
VRYGs.gif


whose solution a research paper writes to be:
ub3j0.gif


Now Integrating factor for solving the differential equation should have been:
EDAPv.gif


And the final solution according to the standard procedure of solving linear homogeneous first order differential equation should have been:
xx9Fv.gif


But in the paper solution is not the same.Please guide me if I am wrong with my justifications.
Also in the final step delta function selects only s=t prime value.I am unable understand why theta function is coming.please elaborate on this step too.Any help will be deeply appreciated. I don't come from a maths background.
 

Answers and Replies

  • #2
somebody please address the issue.thanks in advance.i am utterly confused.
 

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