121k views
3 votes
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.

1 Answer

3 votes

Final answer:

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.

User Shaxrillo
by
7.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories