Given the heat equation $\frac{\partial u}{\partial t} = k\frac{\partial^2 u}{\partial x^2}$ that satisfy boundary conditions $u(0,t) = u(\frac{\pi}{2} ,t)$, find the solution that satisfies the initial condition that $u(x, 0) = \pi sin(3x) - 5sin(42x)$.
Having a little bit of an issue going about this. The initial condition does not satisfy the boundary conditions (plugging in $x=\frac {\pi}{2}$).
Any idea if there's an error in the wording of the question (copied verbatim), or how I would go about solving this?