Question

In: Math

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

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 ′ + 6 y = 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 ′ + 2 y = 0

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

Find the value of y at x = π.

d)

Let y be the solution of the equation y ″ + 6 y ′ + 9 y = 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.

Expert Solution

milcah answered 2 years ago

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