Question

Determine the solutions, if any, to the given boundary value problem.

y′′ +6y′+34y=0; y′(0)=0; y′(π)=0
Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
A. The boundary value problem has a unique solution y(x)=__.
B. The boundary value problem has a one-parameter family of solutions y(x)=__.
C. The boundary value problem has a two-parameter family of solutions y(x)=__.
D. The boundary value problem has no solutions.

Answer 1

To determine the solutions to the given boundary value problem, we can use the boundary conditions and the general forms of the solutions to find the unique solution.

Step-by-step explanation:

To determine the solutions to the given boundary value problem, y'' + 6y' + 34y = 0, with boundary conditions y'(0) = 0 and y'(π) = 0, we can solve for the unknown constants in the general forms of the solutions in regions I and III. Since the walls are rigid and impenetrable, the solution must vanish at the walls, so y(0) = 0 and y(π) = 0. By substituting these conditions into the general forms of the solutions, we can find the unique solution to the boundary value problem.