I have a linear operator $L(p(x)) = -p(x+1) + p(x) + \frac6x \int_0^x p(y) dy$ with eigenvalues of it's representative matrix found to be 6, 3, and 2. From this the respective eigen vectors are (1,0,0) , (1,3,0) , (3,8,4).
I'm asked to find the eigenfunctions for this linear operator. I know that I need to find some function f s.t $L(f) = \lambda f$ but I don't know how to actually do this.
If someone could explain that would be great.