In this introductory course on ordinary differential equations we first provide basic terminologies on the theory of differential equations and then proceed to methods of solving various types of ordinary differential equations we handle first order differential equations and then second order linear differential equations. Into equation 01 yields a 1 v 0 in the above the vector v is known as the eigenvector and the corresponding eigenvalue is found by solving the characteristic equation deta 1 0 if r then the solution with real valued components is given in equation 02 if c ie a ib. In mathematics an ordinary differential equation ode is a differential equation containing one or more functions of one independent variable and the derivatives of those functions the term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable. The idea of factoring an ordinary differential operator or the corresponding linear ordinary differential equation ode into components of lower order originated from the analogous problem for
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