Explanation Given: The Equation are, 2 I ′ 1 ( t ) + 90 I 2 ( t ) = 9 , I ′ 3 ( t ) + 30 I 4 ( t ) − 90 I 2 ( t ) = 0 , 60 I 5 ( t ) − 30 I 4 ( t ) = 0 , I 1 ( t ) = I 2 ( t ) + I 3 ( t ) , I 3 ( t ) = I 4 ( t ) + I 5 ( t ) Calculation: Consider the Equation. I 1 ( t ) = I 2 ( t ) + I 3 ( t ) ... ( 1 ) Substitute I 4 ( t ) + I 5 ( t ) for I 3 ( t ) in Equation (1). I 1 ( t ) = I 2 ( t ) + I 4 ( t ) + I 5 ( t ) … ( 2 ) Consider the Equation. 2 I ′ 1 ( t ) + 90 I 2 ( t ) = 9 … ( 3 ) Substitute I 2 ( t ) + I 4 ( t ) + I 5 ( t ) for I 1 ( t ) in Equation (3). 2 ( I 2 ( t ) + I 4 ( t ) + I 5 ( t ) ) ′ + 90 I 2 ( t ) = 9 2 I ′ 2 ( t ) + 2 I ′ 4 ( t ) + 2 I ′ 5 ( t ) + 90 I 2 ( t ) = 9 … ( 4 ) Consider the Equation. I ′ 3 ( t ) + 30 I 4 ( t ) − 90 I 2 ( t ) = 0 … ( 5 ) Substitute I 4 ( t ) + I 5 ( t ) for I 3 ( t ) in Equation (5). I ′ 4 ( t ) + I ′ 5 ( t ) + 30 I 4 ( t ) − 90 I 2 ( t ) = 0 … ( 6 ) From Equation (4) and Equation (6), 2 I ′ 2 ( t ) − 60 I 4 ( t ) + 270 I 2 ( t ) = 9 … ( 7 ) Substitute 2 I 5 ( t ) for I 4 ( t ) in Equation (5). 2 I ′ 2 ( t ) − 120 I 5 ( t ) + 270 I 2 ( t ) = 9 I ′ 2 ( t ) = 9 2 + 60 I 5 ( t ) − 135 I 2 ( t ) … ( 8 ) Substitute 2 I 5 ( t ) for I 4 ( t ) in Equation (6). I ′ 5 ( t ) = 30 I 2 ( t ) − 20 I 5 ( t ) … ( 9 ) Substitute x 1 for I 2 and x 2 for I 5 in Equation (8) and Equation (9). x ′ 2 = 30 x 1 − 20 x 2 … ( 10 ) x ′ 1 = 9 2 + x 2 − 135 x 1 … ( 11 ) The matrix form of Equation (10) and Equation (11) is, [ x ′ 1 x ′ 2 ] = [ − 135 60 30 − 20 ] [ x 1 x 2 ] + [ 9 2 0 ] Consider the matrix, A = [ − 135 60 30 − 20 ] The characteristic Equation of matrix A is

Fundamentals Of Differential Equations And Boundary Value Problems Plus Mylab Math With Pearson Etext -- Title-specific Access Card Package (7th ... Fundamentals Of Differential Equations)

7th Edition

ISBN: 9780134768717

Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Publisher: PEARSON

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Fundamentals Of Differential Equations And Boundary Value Problems Plus Mylab Math With Pearson Etext -- Title-specific Access Card Package (7th ... Fundamentals Of Differential Equations)

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