MATH24 Lecture 1 - MATH24 Differential Equations...

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Unformatted text preview: MATH24 Differential Equations Definitions An differential equation is an equation involving an unknown function and its derivatives. The following are differential equations involving the unknown function y. 3 5 + = x dx dy 1 2 2 2 2 = + dx dy dx y d e y ( 29 5 sin 4 2 2 3 3 = + + xy dx y d x dx y d x dx dy y dx dy y dx y d 5 3 2 3 7 3 2 2 = + + 4 2 2 2 2 = - x y t y (1.1) (1.2) (1.3) (1.4) (1.5) t E i C dt di R dt i d L cos 1 2 2 = + + (1.6) ( 29 2 2 2 =- + xydy dx y x (1.7) Definitions A differential equation is an ordinary differential equation (ODE) if the unknown function depends on only one independent variable. If the unknown function depends on two or more independent variables, the differential equation is a partial differential equation (PDE). Equations (1.1) through (1.4) are examples of ordinary differential equations, since the unknown function y depends solely on the variable x. Equation (1.5) is a partial differential equation, since y depends on both the independent variables t and x. Definitions In equation 1.6 i is the dependent variable, t the independent variable, and L, R, C, E, and are called parameters . Since the equation 1.7 may be written as or we may consider either variable to be dependent, the other being the independent one....
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This note was uploaded on 01/17/2012 for the course MATH 24 taught by Professor Dantesilva during the Spring '11 term at Mapúa Institute of Technology.

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MATH24 Lecture 1 - MATH24 Differential Equations...

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