Let f(x, y) = u(x, y, 0) be the initial temperature in a thin square plate of side with edges kept at 0C and

Let f(x, y) = u(x, y, 0) be the initial temperature in a thin square plate of side π with edges kept at 0°C and faces perfectly insulated. Separating variables, obtain from u_t = c²∇²u the solution

where