Hi ,
Using Matlab Dsolve function i get that u=0; no beam deflection!
You don't really need "DSolve". The general solution to any linear homogeneous differential equation is a linear combination of the elementary solutions. The conditions that all values be 0 then must give u identically equal to 0 as the solution. (And it should be easy to see that u= 0 for all x does satisfy the equation and additional conditions.)