logistic_guy
Junior Member
- Joined
- Apr 17, 2024
- Messages
- 197
here is the question
Solve the classical differential equation \(\displaystyle u'' - k^2u = f(x), \ \ \ \ a < x < b, \ \ \ \ u(a) = u(b) = 0\).
Hint: \(\displaystyle u(x) = \int_{a}^{b} G(x,s) f(s) \ ds\),
where the function \(\displaystyle G(x,s)\) is known as Green's function for the problem.
my attemp
before and on paper i find \(\displaystyle u(x) = c_1e^{kx} + c_2e^{-kx}\)
how to find particular solution for \(\displaystyle f(x)\)?
Solve the classical differential equation \(\displaystyle u'' - k^2u = f(x), \ \ \ \ a < x < b, \ \ \ \ u(a) = u(b) = 0\).
Hint: \(\displaystyle u(x) = \int_{a}^{b} G(x,s) f(s) \ ds\),
where the function \(\displaystyle G(x,s)\) is known as Green's function for the problem.
my attemp
before and on paper i find \(\displaystyle u(x) = c_1e^{kx} + c_2e^{-kx}\)
how to find particular solution for \(\displaystyle f(x)\)?