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Unformatted text preview: Slide 1 Linear Differential Equations Section 4.1 Preliminary Theory Slide 2 What do we know about linear differential equations? They have a solution. The solution is unique . The solution is defined throughout an interval I. The above statements are true for an initial-value problem. (i.e., we know y , y ’ , y ’’ , etc.) Slide 3 Boundary-Value Problems This is a problem where the dependent variable or its derivatives are specified at different points. Example: Solve subject to: All bets are off! The statements on the previous slide do not hold . ) ( ) ( ) ( ) ( 1 2 x g y x a y x a y x a = + ′ + ′ ′ 1 ) ( , ) ( y b y y a y = = Slide 4 Examples #2 #13 Slide 5 Two Types of Linear Equations Homogeneous Nonhomogeneous ) ( ) ( ) ( ) ( ) ( 1 2 ) 1 ( 1 ) ( = + ′ + ′ ′ + + +-- y x a y x a y x a y x a y x a n n n n ) ( ) ( ) ( ) ( ) ( ) ( 1 2 ) 1 ( 1 ) ( x g y x a y x a y x...
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This note was uploaded on 01/13/2012 for the course MATH 2914 taught by Professor Pamelasatterfield during the Fall '10 term at NorthWest Arkansas Community College.
- Fall '10