$$ u_t-f(t)u_{xx}=0 \textrm{, over } \mathbb{R}^N\times]0,\infty[ \\ u(x,0)=u_0(x)\textrm{, over } x\in \mathbb{R}^N, u_0\in S(\mathbb{R}^N) $$ where $u\in C^2(\mathbb{R}^N\times]0,\infty[)\cap C(\mathbb{R}^N\times[0,\infty[), f\in C^1([0,\infty[), f\geq 0$
This is a exercise of my homework in PDE. I know how to solve this if we don't have this $f(t)$ but with this I'm not knowing how to work here.