Question

Consider the functions:

A. y = 9sin(x)
B. y = sin(9x)
C. y = e^(-9x)
D. y = e^(9x)
Which of the given functions is a solution to (d²y/dx²) = -9²y?

Answer 1

The function that is a solution to (d²y/dx²) = -9²y is y = sin(9x).

Step-by-step explanation:

The function that is a solution to (d²y/dx²) = -9²y is B. y = sin(9x).

To check this, we can take the second derivative of y = sin(9x) and substitute it into the given equation:

d²y/dx² = (9² * -sin(9x)) = -9² * sin(9x)

Now we can compare this with the right side of the equation, which is -9²y:

-9² * sin(9x) = -81 * sin(9x), which is the same as -9²y

Therefore, the function y = sin(9x) is indeed a solution to the given equation.