Hello, 

The problem can be approched by assuming the function as =Csin(kx) +Dsin(kx) and the constant can be obtained by substituting the above equation into equilibrium equation and satisfying for boundary conditions given in the problem. Here is the link for entire problem

https://www.google.co.in/url?sa=t&source=web&rct=j&url=http://home.iitk.ac.in/~madhavr/CHM102/Physical/Lec3.pdf&ved=2ahUKEwiJkYyR_p_fAhWFNY8KHTUNC1YQFjALegQIChAB&usg=AOvVaw2MaaprRBtFftv5cznH6rz_

Hope this helps....