Concepts of Differential Equations

Concepts of Differential Equations - Faculty of Engineering...

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Faculty of Engineering and Technology Chemical Engineering Department 0905321 Mathematical Methods for Chemical Engineering Concepts of Differential Equations 1) A differential equation is an equation involving derivatives of an unknown function of one or more variables. If the unknown function depends on only one variable (so that the derivatives are ordinary derivatives) that equation is called an ordinary differential equation. However, if the unknown function depends on more than one variable (so that the derivatives are partial derivatives) the equation is called a partial differential equation. Example: y x y y x dx dy + = + = 2 or 2 This equation is an ordinary differential equation in which y is the unknown, i.e. y is the dependent variable and x is the independent variable. 0 15 2 2 2 = x dt dx dt x d This equation is an ordinary differential equation in which x is the unknown, i.e. x is the dependent variable and t is the independent variable. V y V x V = + 2 2 2 2 2 This equation is a partial differential equation in which V is the unknown, i.e. V is the dependent variable and x and y are the independent variables. 2) The order of a differential equation is the order of the highest derivative occurring in the equation. Example: y x y y x dx dy + = + = 2 or 2 This equation is first order ordinary differential equation. 0 15 2 2 2 = x dt dx dt x d This equation is a second order ordinary differential equation. V y V x V = + 2 2 2 2 2 This equation is a second order partial differential equation.
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3) The degree of a differential equation is the power to which the highest derivative is raised when the equation has been rationalized and cleared of fractions. Example:
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Concepts of Differential Equations - Faculty of Engineering...

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