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## Homework Statement

So it says solve this wave equation :

[y][/tt] - 4 [y][/xx] = 0

on the domain -infinity<x<infinity

with initial conditions y(x,0) = e^(-x^2), yt(x,0) = x*(e^(-x^2))

## Homework Equations

I used the D Alembert's solution which is 1/2(f(x+ct)+f(x-ct)) + 1/2c ∫ g(z) dz

## The Attempt at a Solution

I just replaced the f in the D'alembert equation by e^(-x^2) and c by 2. To get g(z) I integrated the yt function by substitution method and used x+2t and x-2t as the integral boundaries.

My solution was

y(x,t) = 1/2(e^(-x^2){x+2t}+e^(-x^2){x-2t})+1/2c(-1/2*e^{-(x+2t)^2}+1/2*e^{-(x-2t)^2})

Is this correct? Can someone please confirm or correct me. Please!