( 1 ) Let C 1 and C 2 be arbitrary constants The general solution to the homogeneous differential equation 3 6 1 x 2 y ' ' 2 8 5 x y ' 4 y 0 is the function y ( x ) C 1 y 1 ( x ) C 2 y 2 ( x ) C 1 C 2 ( 2 ) The unique solution to the initial value problem 3 6 1 x 2 y ' ' 2 8 5 x y ' 4 y 0 , y ( 1 ) 3 , y ' ( 1 ) 4 is the function y ( x ) for xin For type inf and for type inf

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( 1 ) Let C 1 and C 2 be arbitrary constants  The general solution to the homogeneous differential equation 3 6 1 x 2 y  '  ' 2 8 5 x y  ' 4 y   0 is the function y ( x )   C 1 y 1 ( x ) C 2 y 2 ( x )   C 1 C 2 ( 2 ) The unique solution to the initial value problem 3 6 1 x 2 y  '  ' 2 8 5 x y  ' 4 y   0 , y ( 1 )   3 , y  ' ( 1 )   4 is the function y ( x )   for xin For   type   inf and for type inf

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( 1 ) Let C 1 and C 2 be arbitrary constants. The general solution to the homogeneous differential equation 3 6 1 x 2

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