consider the diagram above. I know that deflection is described by the equation $$EI\frac{d^4y}{dx^4}=p(x)$$ where $L$ is the length of the beam, $E$ is the Young's module, $I$ is the moment of inertia, $p$ is the distribution of load and $M$ is the torque.
I have the boundary conditions
$y(0)=y'(0)=0$ which means that the left end of the beam is immovable.
$y(L)=0$ which mean that the right end of the beam is supported by something.
Then, what would be the condition for $y'(L)$ ??