$$u(x)-\lambda\int_0^{a}tu(t)dt=f(x)$$
I want to solve generally for u(x) where $\lambda$ and $a$ are parameters and $f(x)$ is given. I have used Laplace transform to get the equation down to: $$U(s)-F(s)=\lambda\int_0^{\infty}e^{-st}\int_0^{a}tu(t)dt$$ I havent taken diff eq in a while so my laplace is a bit rusty. If someone could help me proceed that would be great! a tip to begin with, i think wrestling with this into submission mostly on my own will provide me with some much needed momentum this semester. Thanks in advance