Given the problem: $$(\kappa(x)X^{'})^{'}+\lambda\rho(x)X=0$$ for $0<x<l$ with $X(0)=X(l)=0$ where $\kappa(x)=\kappa_{1}^{2}$ for $x<a$, $\kappa(x)=\kappa_{2}^{2}$ for $\kappa>a$. $\rho(x)=\rho_{1}^{2}$ for $x<a$, and $\rho(x)=\rho_{2}^{2}$ for $x>a$. All these constants are positive and $0<a<l$

The coefficient $\kappa(x)$ and $\rho(x)$ are piecewise functions brings some troubles, how to find the equation to determine the eigenvalue?