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Unformatted text preview: x 1 = y x 2 = y (1) . . . x n = y ( n 1) and x 1 = y x 2 = y (1) . . . x n = y ( n 1) That is, denote the Functions x k = y ( k 1) and constants x k = y ( k 1) For k = 1 , 2 , . . . , n . Then we have the Following system oF diferential equations x 1 = x 2 . . . x n 1 = x n x n = G ( t, x 1 , . . . , x n ) with initial conditions x k ( t ) = x k . In general, iF we have Functions G k such that we have the system x k = G k ( t, x 1 , x 2 , . . . , x n ) , x k ( t ) = x k ; k = 1 , 2 , . . . , m ; we call this a system oF frst order equations . Note that there are m equations and n variables. We say that such a system is a system oF frst order linear equations iF we can write G k ( t, x 1 , x 2 , . . . , x n ) = p k 1 ( t ) x 1 + p k 2 ( t ) x 2 + + p kn ( t ) x n + g k ( t ); k = 1 , 2 , . . . , m. 1...
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue UniversityWest Lafayette.
 Spring '09
 EdrayGoins
 Linear Equations, Equations

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