If f(0) = 8 and L(f(t)) = F(s), thenL[(t – 1)e"-)u(t – 1)f" (t- 1)] =%3D8e -O e*(s - 1)?F' (s – 1)- 2e*(s - 1)F(s – 1)8e -e (s + 1)?F' (s + 1)- 2e*(s + 1)F(s + 1)8 - e*(s – 1)?F' (s - 1)- 2(s – 1)F(s – 1)8els-1) -els-1) (s – 1)2F" (s - 1)- 2els-1) (s – 1)F(s - 1)8e -e(s - 2)2F'(s + 1)- 2e*(s - 2)F(s - 2)

We have to use following formulas to solve given problem:

If f(0) = 8 and L(f(t)) = F(s), then L[(t - 1)e"-)u(t - 1)f" (t- 1)] = 8e- e"(s - 1)2F' (s - 1) - 2e*(s - 1)F(s - 1) 8e - e"(s + 1)2F'(s + 1) - 2e"(s + 1)F(s + 1) 8-e (s-1) F'(s - 1) - 2(s - 1)F(s - 1) Sel-1) - els-1) (s - 1)2F'(s - 1) - 2el-" (s – 1)F(s - 1) 8e - e"(s - 2) F'(s + 1) - 2e*(s - 2)F(s- 2)

If f(0) = 8 and L(f(t)) = F(s), then L[(t - 1)e"-)u(t - 1)f" (t- 1)] = 8e- e"(s - 1)2F' (s - 1) - 2e(s - 1)F(s - 1) 8e - e"(s + 1)2F'(s + 1) - 2e"(s + 1)F(s + 1) 8-e (s-1) F'(s - 1) - 2(s - 1)F(s - 1) Sel-1) - els-1) (s - 1)2F'(s - 1) - 2el-" (s – 1)F(s - 1) 8e - e"(s - 2) F'(s + 1) - 2e(s - 2)F(s- 2)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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