Verify that the differential operator defined by L[y] = y(n) + p1(t) y(n1) + + pn(t) y
Chapter 4, Problem 13(choose chapter or problem)
Verify that the differential operator defined by L[y] = y(n) + p1(t) y(n1) + + pn(t) y is a linear differential operator. That is, show that L[c1 y1 + c2 y2] = 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 combination c1 y1 + + cn yn is also a solution of L[y] = 0.
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