I'm strugling for a while on that. Is there a way to approach analytical the following BVP? $$ \frac{d^4y}{dx^4}+[4\lambda_1^4H(y)+4\lambda_2^4H(-y)]y=0 $$ Where $H(x)$ stands for the Heaviside Step function. i.e. the wavelength changes with respect to the sign of the solution $y(x)$. $C^{(4)}$ continuity must hold.
Any help will be appreciated.