String attatched at x=0 and x=L, string is at rest, initially y is

1) y(0,t)=0

2) y(L,t)=0

Initial conditions: dy/dt=0 with t=0

y(x,0)= 2H*x/L 0<=x<=1/2L

2H(1-x/L) 1/2L<=x<=L

Just struggling to see where the boundary condition y(x,0) is generated from?

I guess it has something to do with the conditions before,

any help will be appreciated, many thanks.