Question: Consider the differential operator L[y] = ry - 6y. (a) (6 pts) Prove that L is a linear differential operator. That is, show why

Consider the differential operator L[y] = ry" - 6y. (a) (6 pts)

Consider the differential operator L[y] = ry" - 6y. (a) (6 pts) Prove that L is a linear differential operator. That is, show why Ly+2]=L[y] + Lz L[ay] = aL[y] for all functions y(x) and z(x) with two derivatives and constants a. (b) (8 pts) Find all values of k so that y = r is a solution to L[y] = xy" - 6y= 0.

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