Here is a simple problem worked out.

Let's take a cantilever beam with uniform distributed load (constant) w=W. Find the deflection curve w(x).

Step 1 -- Calculate boundary conditions V0 and M0.

Input := 

V0 = Integrate[ W, {u,0,L}]

Output =

L W

Input := 

M0 = Integrate[ u W, {u,0,L} ]

Output =

 2
L  W
----
 2

Step 2 -- Calculate y''' curve

Input := 

yppp[x_] = V0 / EI - Integrate[ W/EI, {u,0,x} ]

Output =

L W   W x
--- - ---
EI    EI

Step 3 -- Calculate y'' curve

Input := 

ypp[x_] = M0 / EI  + Integrate[ yppp[u], {u,0,x}]

Output =

 2                2
L  W   L W x   W x
---- + ----- - ----
2 EI    EI     2 EI

Step 4 -- Calculate y' curve

Input := 

yp[x_] = 0 + Integrate[ ypp[u], {u,0,x} ]

Output =

 2            2      3
L  W x   L W x    W x
------ + ------ - ----
 2 EI     2 EI    6 EI

Step 5 -- Calculate y curve

Input := 

y[x_] = 0 + Integrate[ yp[u], {u,0,x} ]

Output =

 2    2        3      4
L  W x    L W x    W x
------- + ------ - -----
 4 EI      6 EI    24 EI

Here is the tip deflection.

Input := 

y[L]

Output =

   4
3 L  W
------
 8 EI