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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The Answer of 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.

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 ) = 0x2ytt+xyt+x2y=0,y(0)=1,yt(0)=0

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