Deflection for entire beam

Problem $2-$

Consider the beam shown in the figure with square cross section of $150$ mm on each side. Determine the deflection of the beam.

Hint. One method to solve the problem is to divide the beam into two regions and then solve the two corresponding differential equations with four boundary conditions $(2$ conditions at A and $2$ conditions at B$)$ plus four continuity conditions at the intersection of the two regions.