I'm going through a mock exam for my finals and have the following heat equation problem:
$\frac{\partial y}{\partial t} = \frac{\partial^2 y}{\partial x^2}, 0<x<1, t>0$
with initial condition $y(x,0) = 0$
and boundary conditions $\frac{\partial y}{\partial x}(0,t) = 0$, $y(1,t) = sin(at)$
Is anyone able to give me some guidance on where to start on where to start on this? I've never seen an example with mixed inhomogeneous boundary conditions and so am not sure where a good place to start is.