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

question 136

Short Answer

The solution of the initial-value problem $x ^ { 2 } y ^ { tt } + x y ^ {t } + x ^ { 2 } y = 0 , y ( 0 ) = 1 , y ^ { t } ( 0 ) = 0$ 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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