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
)
𝑑𝑡] and ℒ
−1
[
4𝑠+5
(𝑠−1)
2(𝑠+2)
]
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