Question

Tools Window Help 35.HEIC (12 documents, 12 total pages) Q Search For Problems 29-38, determine the jorm of the paricile lution y,(x) Do not actually determine the values of the nd the gen-ficients and a par. 29. у"-у, xe 30. y" 4y xe sin 31. y" + 4y (x22 1e sin 2x te 33. y" 4y' +5ysin x 2 Cre 38. y" -2v'y x sin x + x cos x Solutions Using Complex Variables 24 Co There is a nice way to solve linear nonhomogeneous eqationf Co with constant coefficients whose right-hand sides consisfon T and cosine functions. cos gx R sin qx t a s s limi 50% ay" by'cy (31) The idea is to solve a modified equation in which we repiar equation by the complex exponential function Re the sine or cosine term on the right-hand side of the lear inction of the to he ay" + by'+ cy Rex al-value prob- Equation (32) is then solved in the usual m( Deals back solution ta th
38 please show all steps so i can break it down for practice

Answer 1

38 The homoen Ro equation is TX r2-2r + 1 is the charectaristic equation In eqn.① and p(Aeasing tacos n Since the is ws comhmon Aeans in yn (x) = Ax cos x + Bx sin x + C sin x where A,B and C are coefficients