Answer to Question #283544 in Differential Equations for Anu

Question #283544

a) Establish the relation ๐‘‘


๐‘›


๐‘‘๐‘ฅ


๐‘›


(๐‘ฅ


2 โˆ’ 1)


๐‘› = ๐‘›! 2


๐‘› ๐‘ƒ๐‘›(๐‘ฅ)



b) Use Laplace transform to solve


๐‘‘


2๐‘ฆ


๐‘‘๐‘ก


2 + 2


๐‘‘๐‘ฆ


๐‘‘๐‘ก + ๐‘ฆ = ๐‘ก๐‘’


โˆ’๐‘ก ๐‘ค๐‘–๐‘กโ„Ž ๐‘ฆ(0) = 1, ๐‘ฆ


โ€ฒ


(0) = โˆ’2

0
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