I'm trying to solve this equation:$$A\frac{∂^4h}{∂x^4}+B\frac{∂^5h}{∂t∂x^4}+C\frac{∂^2h}{∂t^2}=\frac{∂\delta(x-a)}{∂x}D\sin(\Omega t),$$where $A,B,C,a,D, \Omega $ are constant, $\delta(x)$ is dirc function.
Boundary conditions are:
$[-D+A\frac{∂^2h}{∂x^2}+B\frac{∂^3h}{∂t∂x^2}]_{x=0}=0$, $[-D+A\frac{∂^2h}{∂x^2}+B\frac{∂^3h}{∂t∂x^2}]_{x=l}=0$
$[-D+A\frac{∂^2h}{∂x^3}+B\frac{∂^3h}{∂t∂x^3}]_{x=0}=0$, $[-D+A\frac{∂^2h}{∂x^3}+B\frac{∂^3h}{∂t∂x^3}]_{x=l}=0$
What kind of techniques or methods should I use? Thank you!