Answer to Question #283544 in Differential Equations for Anu

Question #283544

a) Establish the relation 𝑑


𝑛


𝑑π‘₯


𝑛


(π‘₯


2 βˆ’ 1)


𝑛 = 𝑛! 2


𝑛 𝑃𝑛(π‘₯)



b) Use Laplace transform to solve


𝑑


2𝑦


𝑑𝑑


2 + 2


𝑑𝑦


𝑑𝑑 + 𝑦 = 𝑑𝑒


βˆ’π‘‘ π‘€π‘–π‘‘β„Ž 𝑦(0) = 1, 𝑦


β€²


(0) = βˆ’2

0
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