lect138_10_w11

lect138_10_w11 - Wednesday January 26 Lecture 10 :...

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Wednesday January 26 Lecture 10 : Differential equations: Definitions and examples . (Refers to Section 9.2 in your text) Expectations 1. Recognize a solution to a differential equation and an initial value problem. 2. From a direction field of a DE, sketch the curve of the solution to an IVP. 10.1 Definition A differential equation is an equation containing at least one derivative of a variable. The order of a differential equation is the highest order of a derivative which appears in the equation. So a first-order differentiation equation is one where the highest order of the derivative is 1. A differential equation of order 1: A differential equation of order 2: We often use the acronym DE as an abbreviation of the words “differential equation”. Sometimes we use ODE, which stands for “ordinary differential equation” to distinguish from another type of DE called “partial DE” which we do not discuss here. Some differential equations are easily solved since they only require straight integration. For example the differential equation (also written as or has an infinite family of solutions y = cos x + e x + C . - The expression y = cos x + e x + C actually represents the complete family or complete set of solutions to the DE - If we choose C = 2 for example the expression y = cos x + e x + 2 is a particular solution to the DE.
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When presented with a differential equation we normally want to solve it, if possible,
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lect138_10_w11 - Wednesday January 26 Lecture 10 :...

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