Boundary Conditions for Wave Solution

Given an arbitrary harmonic solution to the wave equation

y(x,t)=Asin(xvt)+Bsin(x+vt),y(x,t) = A \sin (x-vt) + B \sin (x+vt),

find the general solution, i.e. find the coefficients AA and BB given the following boundary conditions:

y(0,t)=0,y(L,0)=1.y(0,t) = 0, \qquad y(L,0) = 1.

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