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Dirichlet boundary conditions correspond to setting the derivative coefficients to zero ($\alpha_2 = \beta_2 = 0$), leaving conditions on the values of $y$ at the endpoints. Neumann boundary conditions correspond to setting the function coefficients to zero ($\alpha_1 = \beta_1 = 0$), leaving conditions on the derivatives.

Conditions: The general boundary conditions are $\alpha_1 y(a) + \alpha_2 y'(a) = 0$ and $\beta_1 y(b) + \beta_2 y'(b) = 0$.; Dirichlet: $\alpha_2 = \beta_2 = 0$.; Neumann: $\alpha_1 = \beta_1 = 0$.

Dirichlet boundary conditions correspond to setting the derivative coefficients to zero ($\alpha_2 = \beta_2 = 0$), leaving conditions on the values of $y$ at the endpoints. Neumann boundary conditions correspond to setting the function coefficients to zero ($\alpha_1 = \beta_1 = 0$), leaving conditions on the derivatives.

Conditions: The general boundary conditions are $\alpha_1 y(a) + \alpha_2 y'(a) = 0$ and $\beta_1 y(b) + \beta_2 y'(b) = 0$.; Dirichlet: $\alpha_2 = \beta_2 = 0$.; Neumann: $\alpha_1 = \beta_1 = 0$.