f(D) is a differential operator with constant coefficients
If \(m\) is any root of \(f(m) = 0\) , then \(f(D)e^{mx} = 0\), which means that \(y = e^{mx}\) is a solution of equation.
For details, please check on solitaryroad.com. My notes are clues for myself. They are readable and reproducible for myself. I do not want to write too much.