Answer to Question #174406 in Differential Equations for Naveen

Question #174406

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

cos 4x




1
Expert's answer
2021-03-31T15:27:11-0400

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

Then for y=cos4xy = cos4x :

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

Hence, this linear differential operator annihilates the given function.


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