Heated rod problem

ab959

1. The problem statement, all variables and given/known data

I was asked to write the equation that describes the following heated rod: Two rods of different materials that have been fused together on the x-axis at x=0 to form one rod of infinite length.

I was thinking of just using the heat equation integrated from -infinity to 0 with k1 and 0 to +infinity with k2 and having the solution as the sum of these two integrals.

I am really quite unsure of how to go about solving this so any help would be much appreciated.