Solve the governing differential equations (in terms of displacements) for the beam shown and subjected to a parabolic distributed load (with values of 0 kN/m at the supports and 10 kN/m at mid-span)....

Solve the governing differential equations (in terms of displacements) for the beam shown and subjected to a parabolic distributed load (with values of 0 kN/m at the supports and 10 kN/m at mid-span). Determine the expressions for the axial displacement and deflection and the support reactions. Assume A, I and E are constant throughout.