In the 10th lecture we are asked to consider

$$

0=\int_{II}G(x,y,t-\tau)(-u_{\tau}(y,\tau))+ku_{yy}(y,\tau)d\tau'dy

$$

1. question: What are we integrating over here? Is $\tau'=t-\tau$?

2. Where is this expression coming from? Is it a trial solution that I simply have to take as given, or does it follwow from any other expression?

Thanks!