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Solve the given system of equations. Assume t > 0. tx' = Ax is analogous to the second order Euler equation. Assuming that x = &t", where is a constant vector, & Hint: The system tx' = and r must satisfy (A – rI)§ = 0 in order to obtain nontrivial solutions of the given differential equation. x = c1 A + C2 ,-2 1 x = C1 -1 + c2 4 x = c | |t + c2 X = C1 12 + C2 (:). X = c1 t + c2

Solve the given system of equations. Assume t > 0. tx' = Ax is analogous to the second order Euler equation. Assuming that x = &t", where is a constant vector, & Hint: The system tx' = and r must satisfy (A – rI)§ = 0 in order to obtain nontrivial solutions of the given differential equation. x = c1 A + C2 ,-2 1 x = C1 -1 + c2 4 x = c | |t + c2 X = C1 12 + C2 (:). X = c1 t + c2

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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Solve the given system of equations. Assume t > 0. -1 tx' = 8 -3 Hint: The system tx' and r must satisfy (A – rI)§ = 0 in order to obtain nontrivial solutions of the given differential equation. = Ax is analogous to the second order Euler equation. Assuming that x = &t, where g is a constant vector, & X = c1 + c2 2. 1 |t + c2 X = c| () (:)- (:) 1 t + c2 4 -1 X = c1 2 + C2 2. X = c1 X = c1 t + c2 -1
Transcribed Image Text:Solve the given system of equations. Assume t > 0. -1 tx' = 8 -3 Hint: The system tx' and r must satisfy (A – rI)§ = 0 in order to obtain nontrivial solutions of the given differential equation. = Ax is analogous to the second order Euler equation. Assuming that x = &t, where g is a constant vector, & X = c1 + c2 2. 1 |t + c2 X = c| () (:)- (:) 1 t + c2 4 -1 X = c1 2 + C2 2. X = c1 X = c1 t + c2 -1
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