Boundary value problem

Main Question or Discussion Point

let be the two boundary value problem

$$-D^{2}y(x)+f(x)y(x)= \lambda _{n} y(x)$$

with $$y(0)=0=y(\infty)$$

and the same problem $$-D^{2}y(x)+f(x)y(x)= \beta _{n} y(x)$$

with $$y(-\infty)=0=y(\infty)$$

i assume that in both cases the problem is SOLVABLE , so my question is , are the eigenvalues in both cases equal ? , i mean $$\lambda _{n} = \beta _{n}$$ , or have the same dependence on parameter 'n' ?