Question: diving board problem differential what am i doing wrong

I have a beam rigidly secured at one end (a diving board) and want to find the deflection of the beam when a mass is applied at the end. 

I have the differential equation

eq := diff(v(x), x, x) = P*x/(E*Iz) # E youngs modulus and Iz the moment properties of the diving board. 

The solution says to integrate to get deflected slope of the board.

int(rhs(eq))

but the answer shows a constant of integration c1.  Where did it go? 

Then apply a boundary condition x=0, slope is fixed = 0 and we find that c1

c1= - P*L^2/(E*Iz*2)

plug c1 back into our integrated equation and we get  dv/dx  = P(x^2-L^2)/(2*E*Iz)

integrate again to get a displacement equation, and solving c2 in that eq with the boundary condition that when x=L v=0 the solution is

v=(P/E*Iz)*( x³/6 - L²*x/2 + L³/3 )

However I can't seem to get that.  I tried a shorter route with dsolve ( I show below) but that didn't seem to come out right.  Where am I going wrong?

eq := diff(v(x), x, x) = P*x/(E*Iz):

bcs:=v(L)=0,v'(0)=0  # the second boundary condition when x=L v=0 and the first condition x=L slope=0

dsolve({eq,bcs})

Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: {v(L), v(x)}

What am I doing wrong?