I am trying to identify natural and essential boundary conditions from this differential equation.

Strong form is :
$$\frac{d^2}{dx^2} \bigg[R(x)\frac{d^2w}{dx^2}\bigg] - q(x) =0, \hspace{6pt}\text{for } 0<x<L
$$ 
(This is Euler-Bernoulli beam equation. )
Subjected to boundary conditions:
$$w(0)=0, \hspace{10pt} \bigg(\frac{dw}{dx}\bigg)\_{x=0} =0, \hspace{10pt} \bigg(b\frac{d^2w}{dx^2}\bigg)\_{x=L}=M, \hspace{10pt} 
\bigg [ \frac{d}{dx} \bigg (b\frac{d^2w}{dx^2}\bigg)\bigg ]\_{x=L}=F$$

To get the weak form, I multiply first equation by weight function $v$ and get following weak form after some algebra,

$$\int\_0^L \bigg[b\frac{d^2v}{dx^2}\frac{d^2w}{dx^2}-vq \bigg]dx + \bigg[v\frac{d}{dx}\bigg(b\frac{d^2w}{dx^2} \bigg) - b\frac{dv}{dx}\frac{d^2w}{dx^2} \bigg]\_0^L
$$ 

My question is: in the boundary conditions listed, which one are natural and essential boundary conditions? And how to identify that? In the second order ODE, there are two boundary conditions. And the one having derivative term is essential boundary condition. But in higher order ODE, I am not sure how to identify this when there are multiple boundary conditions involving derivatives.