Verify that the differential operator defined byL[y] = y(n) + p1(t)y(n1) ++ pn(t)yis a
Chapter 4, Problem 18(choose chapter or problem)
Verify that the differential operator defined byL[y] = y(n) + p1(t)y(n1) ++ pn(t)yis a linear differential operator. That is, show thatL[c1y1 + c2y2] = c1L[y1] + c2L[y2],where y1 and y2 are n-times-differentiable functions and c1 and c2 are arbitrary constants.Hence, show that if y1, y2, ... , yn are solutions of L[y] = 0, then the linear combinationc1y1 ++ cnyn is also a solution of L[y] = 0.
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