Answer to Question #174406 in Differential Equations for Naveen

Question

Find a linear differential operator that annihilates the given function. (Use D for the differential operator.)

cos 4x

Answer 1

Consider operator D such that: $Dy = y'' + 16y$

Then for $y = cos4x$ :

$Dy = (cos4x)'' + 16 cos4x = -16cos4x + 16 cos4x = 0 \ \forall x$

Hence, this linear differential operator annihilates the given function.