Question

The following second order ordinary differential equation has the boundary conditions: \[ y(0) = 0, \quad y(1) = 1 \] The type of the above boundary conditions is:

• A. Neumann
• B. Dirichlet
• C. Cauchy
• D. Robin

Hint:

Dirichlet boundary conditions specify the values of the solution at the boundaries, while Neumann boundary conditions specify the derivative of the solution at the boundaries.

Answer 1

The Correct Option is B

The given boundary conditions are: \[ y(0) = 0, \quad y(1) = 1 \] Step 1: Understanding Boundary Conditions.
- Neumann Boundary Condition specifies the derivative (rate of change) of the solution at the boundaries. - Dirichlet Boundary Condition specifies the value of the solution at the boundaries. - Cauchy Boundary Condition is a combination of initial and boundary conditions for first-order equations. - Robin Boundary Condition is a weighted combination of Dirichlet and Neumann conditions. Step 2: Conclusion.
Since the boundary conditions are given in terms of the function's values, i.e., \( y(0) = 0 \) and \( y(1) = 1 \), these are Dirichlet boundary conditions.