Find a linear differential operator that annihilates the given function. (Use D for the differential operator.)
cos 4x
Consider operator D such that: Dy=y′′+16yDy = y'' + 16yDy=y′′+16y
Then for y=cos4xy = cos4xy=cos4x :
Dy=(cos4x)′′+16cos4x=−16cos4x+16cos4x=0 ∀xDy = (cos4x)'' + 16 cos4x = -16cos4x + 16 cos4x = 0 \ \forall xDy=(cos4x)′′+16cos4x=−16cos4x+16cos4x=0 ∀x
Hence, this linear differential operator annihilates the given function.
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