Solution to a wave equation

Let u be a solution of the wave equation utt-uxx=0 on the whole plane. Suppose that ux(x,t) is a constant on the line x=1+t. Assume that u(x,0)=1 for all x in R and u(1,1,)=3. Find such a solution u.

I need help trying to incorporate the ux(x,t) is a constant on the line x=1+t

Answers and Replies

So I got this as a solution by plugging it into an equation for wave equations with a Neumann condition:

u(x,t)= t+1/2(4t+2t^2) x>0

u(x,t)= t+1/2(3/2+5t+3t^2/2) 0<x<t