You've got the gist.
Since v=0 at x=0, C2 = 0
And using symmetry, dy/dx = 0 at x=(L1/2 + L2). Use this to solve for C3.
Now just equate the vertical displacements and gradients at the point where q starts to solve for your remaining constants. 2 unknown constants, 2 equations, and you're done.
You can work out the solution analytically.
The first portion L2 of the beam is easy enough. You only have a shear force from the support to give moments. Get the moment equation, integrate it to get displacement as a function of x. Obtain also the moment M1 at the point where q starts, ie...
I think you are getting RA and time mixed up.
RA looks like time, but it is really a coordinate system fixed on the stars.
As the Earth rotates, it is also revolving around the sun. This causes the constellations to rise about 4 minutes earlier each night.
Suppose a star has RA = 6hr...