Question

Find the correct boundary conditions on a function y(x) solution of a periodic а Sturm-Liouville system on the interval [2, 3].

O y(2) +y'(2) = -, y(3) +y' (3) =
O y(2) = y(3), y' (2) = y' (3).
O y(2) = y(2) + 2, y(3) = y'(3) + 2
O y(2) + y'(2) = 0, y(3) + y'(3) = 0.
O y(2) = y'(2), y(3) = y'(3).
O None of the options displayed.
O y(2) = y'(3), y(3) = y' (2).

Answer 1

The correct boundary conditions on a function y(x) solution of a periodic Sturm-Liouville system on the interval [2, 3] are y(2) = y(3) and y'(2) = y'(3).

Step-by-step explanation:

The correct boundary conditions on a function y(x) solution of a periodic Sturm-Liouville system on the interval [2, 3] are y(2) = y(3) and y'(2) = y'(3).

Boundary conditions are the conditions that must be satisfied at the boundaries of a system. In this case, the boundary conditions require that the value of the function and its derivative are equal at both boundaries. This ensures that the function is continuous and differentiable throughout the interval.

For example, if we have a function y(x) that satisfies the Sturm-Liouville system and y(2) = 5 and y(3) = 6, then the derivative of y at x=2 must be equal to the derivative of y at x=3, in order to satisfy the boundary conditions.