Question

Find a linear differential operator that annihilates the given function :

1+7e^(2x)

I know its (D-2) for e^2x but can you explain why it is D(D-2)

Answer 1

D(D-2)=D^2-2D
so:
(D^2-2D)(1+7e^(2x))=D^2(1+7e^(2x))-2D(1+7e^2x)=28e^(2x)-28e^(2x)=0

Answer 2

@Annihilator