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of A By computing the fundamental matrix, show that the matrix exponential is eAt = (¹ 1 + 2t t -4t 1-2t = - ( ² = 1) 1 +).

of A By computing the fundamental matrix, show that the matrix exponential is eAt = (¹ 1 + 2t t -4t 1-2t = - ( ² = 1) 1 +).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. Fundamental (a) of A ODES matrices By computing the fundamental matrix, show that the matrix exponential 2-4 -4t 1 + 2t ( 1 =1) is eA² = (¹ + +). -2 t Hence show that the solution to the non-homogeneous system of (361²) 6t x' = Ax + with initial condition ¹ x (0) = ( 8 ) is x1 1 - 2t = 8t³ + 6t4, x₂ = 3t² − 2t³ + 3t4.
Transcribed Image Text:4. Fundamental (a) of A ODES matrices By computing the fundamental matrix, show that the matrix exponential 2-4 -4t 1 + 2t ( 1 =1) is eA² = (¹ + +). -2 t Hence show that the solution to the non-homogeneous system of (361²) 6t x' = Ax + with initial condition ¹ x (0) = ( 8 ) is x1 1 - 2t = 8t³ + 6t4, x₂ = 3t² − 2t³ + 3t4.
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