EI {d⁴y(x,t)/dx⁴ } +CA{d² y(x,t)/dx²}= summation of (F_o (sin(5nvt/r)sin(nwt)))  from n=1 to n= infinity

the derivative here are partial not ordinary

where EI, CA ,F_o , v ,r and w are constants 

the boundry conditions are : y(0,t)=0 and y(r,t) =0 .

and the initial conditions are :

y(x,0)=0  ,dy(x,0)/dt= 0