Consider L = d2 dx2 + 6 d dx + 9. (a) Show that L(erx)=(r + 3)2erx. (b) Use part (a) to
Chapter 5, Problem 5.5.5(choose chapter or problem)
Consider L = d2 dx2 + 6 d dx + 9. (a) Show that L(erx)=(r + 3)2erx. (b) Use part (a) to obtain solutions of L(y) = 0 (a second-order constant-coefficient differential equation). (c) If z depends on x and a parameter r, show that rL(z) = L z r . (d) Using part (c), evaluate L(z/r) if z = erx. (e) Obtain a second solution of L(y) = 0, using part (d).
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