a) Establish the relation ๐
๐
๐๐ฅ
๐
(๐ฅ
2 โ 1)
๐ = ๐! 2
๐ ๐๐(๐ฅ)
b) Use Laplace transform to solve
๐
2๐ฆ
๐๐ก
2 + 2
๐๐ฆ
๐๐ก + ๐ฆ = ๐ก๐
โ๐ก ๐ค๐๐กโ ๐ฆ(0) = 1, ๐ฆ
โฒ
(0) = โ2
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