(a) Let D = , and an, an-1,..., a1, ao E R. Is anx" D" + an-1x"-1Dn-1+ ... + a1xD+ ao a linear operator? Prove or provide a counterexample. dx ' (b) Find an operator A that annihlates the following functions. i. In(x) ii. ta , α R iii. sin(3 In(x)) (c) Solve the following using the annihlator method. i. y" +3y' + 2y = 5 In(x) ii. x'y" + 7xy' + 10y = 4x? cos(3lIn(x)) + x-3

(a) Let D = , and an, an-1,..., a1, ao E R. Is anx" D" + an-1x"-1Dn-1+ ... + a1xD+ ao a linear operator? Prove or provide a counterexample. dx ' (b) Find an operator A that annihlates the following functions. i. In(x) ii. ta , α R iii. sin(3 In(x)) (c) Solve the following using the annihlator method. i. y" +3y' + 2y = 5 In(x) ii. x'y" + 7xy' + 10y = 4x? cos(3lIn(x)) + x-3

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 51E

See similar textbooks