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  3. a) find the value of the wronskian of the function

a) Find the value of the Wronskian of the functions  f = x^7 and g = x^8 at the...

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Basic Math

a)

Find the value of the Wronskian of the functions  f =x^7

and g = x^8 at the piont  x = 1.

b)

Let  y be the solution of the equation y ? ? 5 y ? + 6y = 0

satisfying the conditions y ( 0 ) = 1 and y ? ( 0 ) = 2.

Find ln ? ( y ( 1 ) ).

c)

Let y be the solution of the equation  y ? + 2 y ? + 2y = 0

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

Find the value of  y at x = ?.

d)

Let y be the solution of the equation  y ? + 6 y ? + 9y = 0

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

Find the value of the function   f ( x ) = ln [(y(x))/(x)] at  x = 1.

e)

One of solutions of the equation y ? ? y ? + y = x^2 + 3x +5

is a function of the form y = A*x^2 + B*x + C.

Find the value of the coefficient C.

f)

One of solutions of the equation y ? ? 2 y ? + 2 y = ( x + 1 )e^x

is a function of the form y = ( A*x + B ) e^x.

Find the value of the coefficient B.

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