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Consider the operation L on functions f(t) under the definition d² f dt² df L(f(t)) = f(t) + + dt That is, we can express L as: d dt dt² L:=1+ + (a) Compute L(t³ – t²). (b) Express L(tan(t)) in terms of cos(t) and sin(t). (c) Compute L(ect) and express in factorised form. (d) For what values c ER does L(ect) = ect?

Consider the operation L on functions f(t) under the definition d² f dt² df L(f(t)) = f(t) + + dt That is, we can express L as: d dt dt² L:=1+ + (a) Compute L(t³ – t²). (b) Express L(tan(t)) in terms of cos(t) and sin(t). (c) Compute L(ect) and express in factorised form. (d) For what values c ER does L(ect) = ect?

Advanced Engineering Mathematics
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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Could someone give me solution for the question below maybe only a and b if not all of them , 

tahnks.

Consider the operation L on functions f(t) under the definition d² f dt² df L(f(t)) = f(t) + + dt That is, we can express L as: d dt dt² L:=1+ + (a) Compute L(t³ – t²). (b) Express L(tan(t)) in terms of cos(t) and sin(t). (c) Compute L(ect) and express in factorised form. (d) For what values c ER does L(ect) = ect?
Transcribed Image Text:Consider the operation L on functions f(t) under the definition d² f dt² df L(f(t)) = f(t) + + dt That is, we can express L as: d dt dt² L:=1+ + (a) Compute L(t³ – t²). (b) Express L(tan(t)) in terms of cos(t) and sin(t). (c) Compute L(ect) and express in factorised form. (d) For what values c ER does L(ect) = ect?
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