The displacement y(x,t) of a semi-infinite elastic string is determined from the following problem
⎩
⎨
⎧
∂t
2
∂
2
y
=
9
1
∂x
2
∂
2
y
−32,
y(0,t)=0,lim
x→[infinity]
∂x
∂y
=0,t>0,
y(x,0)=0,
∂t
∂y
∣
∣
t=0
=0,x>0.
x>0,t>0,
Use the Laplace transform method to find the displacement y(x,t).