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The Solution of the Initial-Value Problem x2ytt+xyt+x2y=0,y(0)=1,yt(0)=0x ^ { 2 } y ^ {tt } + x y ^ { t } + x ^ { 2 } y = 0 , y ( 0 ) = 1 , y ^ { t } ( 0 ) = 0

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The solution of the initial-value problem x2ytt+xyt+x2y=0,y(0)=1,yt(0)=0x ^ { 2 } y ^ {tt } + x y ^ { t } + x ^ { 2 } y = 0 , y ( 0 ) = 1 , y ^ { t } ( 0 ) = 0 is called a Bessel function of order 0 . Solve the initial - value problem to find a power series expansion for the Bessel function.

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Definitions:

Annual Depreciation

The portion of an asset's cost that is allocated as an expense each year over its useful life through the process of depreciation.

Salvage Values

Salvage Values represent the estimated residual value of an asset after its useful life has ended and it has been fully depreciated.

Useful Lives

The estimated periods of time over which fixed assets, such as machinery or buildings, are expected to be used by a business.

Straight-line Method

A method of calculating depreciation or amortization by evenly distributing the cost of an asset over its expected useful life.

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