The Question is:
A uniform horizontal beam OA, of length $a$ and weight $w$ per unit length is clamped horizontally at O and freely supported at A. The transverse displacement $y$ of the beam is governed by the differential equation
where $x$ is the distance along the beam measured from O, $R$ is the reaction at A, and $E$ and $I$ are physical constants.
After this they give a boundary conditions, and as one expects, to solve the equation - the maths which I have successfully completed.
My question is the description of how the beam is restricted and in which directions it can move - I don't seem to understand the mechanics of the beam.