By taking particle derivatives of this function w.r.t. x and `t`
`(del^(2)y)/(delx^(2))=(12(x-3t)^(2)-4)/([((x-3t)^(2)+1)]^(3))` and `(del^(2)y)/(delt^(2))=(108(x-3t)^(2)-36)/([(x-3t)^(2)+1]^(3))`
or `(del^(2)y)/(delx^(2))=(1)/(9) (del^(2)y)/(delt^(2)`
comparing with linear wave equation, we see that the wave function is a solution to the linear wave equation if the speed at which the pulse moves is `3 cm//s`. it is apparent from wave function therefore it is a solution to the linear wave equation.
