Answer to Question #283545 in Differential Equations for Anu

Question

a) Obtain power series solution in powers of 𝑥 for

(𝑥

2 − 1) 𝑦

′′ + 3𝑥 𝑦

′ + 𝑥𝑦 = 0, 𝑦(0) = 4, 𝑦

′

(0) = 6

b) Find ℒ[𝑒

4𝑡 ∫ (

1−cos 2𝑡

𝑡

)

𝑡

𝑑𝑡] and ℒ

−1

[

4𝑠+5

(𝑠−1)

2(𝑠+2)

]