open interval I gives rise to the succession of derivatives: dx d'x d'X X= X, dt dtdt Now a differential equation in the function X t is therefore an equation of the type: MATHEMATICS 1 dx dX d*X X =0 ......... (1) dt dr drk Such an equation is said to be an ordinary differential equation. Thus an ordinary differential equation is a differential equation in which the constituent function X: X(t) is a function of a single real variable. We often use the acronym ODE in place of the full term: ordinary differential equation. II) On the other hand, there are differential equations in a function u:xux of a real multivariable xxxx, which ranges in an open subset of R". Such a function u=ux gives rise to mixed partial derivatives: ,1in. Ju -j1