Example The temperature u=u(x,t)of a long thin uniform rod satisfies du 2u 01-kx2 where k is the thermal diffusivity of the rod. 4日10y4至，1无2000 Ordinary Differential EquationsExample The temperature u = u(x,t) of a long thin uniform rod satisfies ∂u ∂ t = k ∂ 2u ∂ x 2 , where k is the thermal diffusivity of the rod. Definition (PDE) Partial differential equations: differential equations that involve an unknown function of more than one independent variables, together with partial derivatives of the function. Ordinary Differential Equations