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  3. a) the functions y1 = x^2 and y2 = x^5 are two sol

a) The functions y1 = x^2 and y2 = x^5 are two solutions of the equation x^2 y...

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Basic Math

a)

The functions y1 = x^2 and y2 = x^5 aretwo solutions of the equation

x^2 y ? ? 6 x y ? + 10 y = 0.

Let  y be the solution of the equation x^2 y ? ? 6 x y? + 10 y = 3 x^5

satisfyng the conditions y ( 1 ) = 0 and  y ? ( 1 ) =1.

Find the value of the function  f ( x ) = y ( x ) / ln?( x ) at  x = 2.

b)

The function y1 = x^5 is a solution of theequation

x^2 y ? ? 11 x y ? + 35 y = 0.

Let  y2 be the solution of this equationsatisfying the conditions

y2 ( 1 ) = 0 and y2 ? ( 1 ) = 2.

Find the value of y2 at x = 2.

c )

The function y1 = x^7 is a solution of theequation

x^2 y ? ? 8 x y ? + 14 y = 0.

Let  y2 be the solution of this equationsatisfying the conditions

y2 ( 1 ) = 1 and y2 ? ( 1 ) = 2.

Find the value of y2 at x = 2.

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