Question

In: Math

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

a)

The functions y₁ = x^2 and y₂ = x^5 are two 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 the equation

x^2 y ″ − 11 x y ′ + 35 y = 0.

Let y₂ be the solution of this equation satisfying 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 the equation

x^2 y ″ − 8 x y ′ + 14 y = 0.

Let y₂ be the solution of this equation satisfying the conditions

y₂ ( 1 ) = 1 and y₂ ′ ( 1 ) = 2.

Find the value of y₂ at x = 2.

Expert Solution

milcah answered 2 years ago

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