Within the general framework of a multifactor term structure model, the fundamental partial differential equation (PDE) satisfied by a default-free zero-coupon bond price is derived via a martingale-oriented approach. Using this PDE, a result characterizing a model belonging to an exponential affine class is established using only a system of partial derivatives. It is also shown that the solution to the bond price PDE has the conditional expectation representation arising in martingale pricing through the application of a multi-dimensional version of Ito's lemma and a property of the stochastic integral.