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Find the general solution of the system of equations X' - ( 205 ) x + ( 10 ) e²¹. est.

Find the general solution of the system of equations X' - ( 205 ) x + ( 10 ) e²¹. est.

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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Question

Find the general solution to the system of equations

Find the general solution of the system of equations X' (50 5 )x - ( 10 ) e*. X = Choose one + (-1/₁2) ₁ 1 15t + C₂ ( 2₁ ) e¹0² + 1/ ( 2 ) e°( е est 4 1 c₁ ( ²2 ) ² ² + 0₂ ( ₂2 ) ²¹²5² + 1/ ( 1²8 ) ** -5t C1 1 15t €₂ est 4 1 a ( ¹2 ) ² + 0₂ ( 2² ) e - 10²4 + 1/ ( ¹8 ) te ³ 5t 1 -15t 1 -2 -8 test 5t C1 (1) ²+(₁) + (1) 1 C₂ -15t 2 ²² 5t -2 est 4 2 a₁ ( 1 ) e -5t C1 ² + 1 C₂ 2 ( ²₁2 ) e²5¹ + ²/1 ( ² ) e ³² 15t 2 5t -2 C1 = 20 5 -5t
Transcribed Image Text:Find the general solution of the system of equations X' (50 5 )x - ( 10 ) e*. X = Choose one + (-1/₁2) ₁ 1 15t + C₂ ( 2₁ ) e¹0² + 1/ ( 2 ) e°( е est 4 1 c₁ ( ²2 ) ² ² + 0₂ ( ₂2 ) ²¹²5² + 1/ ( 1²8 ) ** -5t C1 1 15t €₂ est 4 1 a ( ¹2 ) ² + 0₂ ( 2² ) e - 10²4 + 1/ ( ¹8 ) te ³ 5t 1 -15t 1 -2 -8 test 5t C1 (1) ²+(₁) + (1) 1 C₂ -15t 2 ²² 5t -2 est 4 2 a₁ ( 1 ) e -5t C1 ² + 1 C₂ 2 ( ²₁2 ) e²5¹ + ²/1 ( ² ) e ³² 15t 2 5t -2 C1 = 20 5 -5t
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