Sunday, 20 May 2018

ORDINARY DIFFERENTIAL EQUATIONS HAND WRITTEN NOTE BY PI AIM INSTITUTE

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.


Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics are solutions of linear differential equations (see Holonomic function). When physical phenomena are modeled with non-linear equations, they are generally approximated by linear differential equations for an easier solution. The few non-linear ODEs that can be solved explicitly are generally solved by transforming the equation into an equivalent linear ODE (see, for example Riccati equation).

Some ODEs may be solved explicitly in terms of known functions and integrals. When it is not possible, one may often use the equation for computing the Taylor series of the solutions. For applied problems, one generally use numerical methods for ordinary differential equations for getting an approximation of the desired solution.

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