Lectur15 - Lecture XV Review of Dynamic Mathematics II I....

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Lecture XV Review of Dynamic Mathematics II I. Examples A. Homogeneous First Order Linear Differential Equations 1. Example 1: & xx += 30 Proposed solution xt Ae t () = - 3 Given an initial value of x(0) = 5, what is the value of A? Check the solution: (29 e e x t e e t t tt ’( ) ( ) = =- - + = - - -- 5 15 31 5 3 5 0 3 3 33 2. Example 2: & 60 Proposed solution t = - 6 Given the initial value of x(0)=4, what is the value of A? Check the solution: e e xt x t e e t t = - + - - 4 24 24 6 4 6 6 66 B. Non Homogeneous First Order Linear Differential Equations with a Constant Right Hand Side 1. Example 1: & 36 Proposed solution x e t + - 0 3 6 3 6 3 What is the particular solution to this problem? What is the complementary solution to this problem? Given an initial condition of x(0)=5, check the solution: e e e x t e e t t t + =+ -+ + = - - - 52 2 32 9 39 3 3 2 6 3 3 3 2. Could you solve for the initial conditions, if you where given x(2) = 10?
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(29 xx e xe () 22 2 1 0 10 2 2 0 4 0 4 =- + = + - 3. Example 2: & += 66 Proposed solution xt x e t + - 0 6 6 6 6 6 Taking the initial solution of x(0)=4 and checking the solution: e e x t e e t t tt ’( ) ( ) =+ - + + = - - -- 31 18 61 8 6 3 1 6 6 6 C. Non Homogeneous First Order Linear Differential Equations with a Variable Right Hand Side 1. Example 1: & xxt e t + - 1
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This note was uploaded on 11/08/2011 for the course AEB 6533 taught by Professor Moss during the Fall '08 term at University of Florida.

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Lectur15 - Lecture XV Review of Dynamic Mathematics II I....

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