- #1
Domdamo
- 12
- 0
- Homework Statement
- We have the equation
f1(x)-f1(x-pi)=f2(x)
where f1, f2 are the unknown and the known functions, respectively.
f1, f2 are periodic functions with period 2pi.
Is it possible to determine the explicit formula of f1?
If yes how should we calculate it?
- Relevant Equations
- [1]
f1(x)-f1(x-pi)=f2(x)
[2]
f1(x)=f1(x+2pi)
[3]
f2(x)=f2(x+2pi)
Laplace transform of eq. [1]
[4]
F1(p)-exp{-pi*p}*F1(p) = F2(p)
Rearranging eq. [4]
[5]
F1(p) = frac{1}{1-exp{-pi*p}}*F2(p)
Inverse LT of eq. [5]
[4]
F1(p)-exp{-pi*p}*F1(p) = F2(p)
Rearranging eq. [4]
[5]
F1(p) = frac{1}{1-exp{-pi*p}}*F2(p)
Inverse LT of eq. [5]