ENGR 213 Lecture Notes - Lecture 1: Partial Differential Equation, Dependent And Independent Variables, Boundary Value Problem
22 Apr 2016
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Deffinition: an ordinary differential equation (ode) is an equation which involves one unknown function (dependent variable), say y, and one or more derivatives of y taken with respect to an independent variable, say x. A partial differential equation (pde) is one, which contains partial derivatives. If the primes are replaced by dots then we have. If f is a real valued function given by then. The order of the highest derivative appearing in the equation it indicates the order of the ode. Therefore, the order of the equation under consideration is n. The above equation is linear because the power of the dependent variable y and all its derivatives are one. Linear ode of order 2 is an ode of order 4, due to sin y term the equation is non linear. Let us now consider the normal form of the equation. A second integration will result into: while a third integration will give:
