Consider a system of differential equations which has the general solution:= C1e-5-t + C2-1(a) Determine the fundamental matrix O (t) which has the property (0) = I.15 2t8-5t15-5t8(t) =112t-5tе+8(b) Use the fundamental matrix found in part (a) to quickly determine the particular solution for the following initial conditions:a (t) = 3e-5ty (t) =2t;8]-[?x (0)(ii)x (t) =y (t) =

Given: The system of general solution is xtyt=C1 31e-5t+C2 5-1 e2t

Consider a system of differential equations which has the general solution: :8]-« [}]; 5 e-5+ +C2 C1 (a) Determine the fundamental matrix ¢ (t) which has the property (0) = I. -5t e2t + 8 15 -5t - 15 21 3 8 8 8. * (t) = || 1,2t 8 -5t 5 -5t + 3 2t - (b) Use the fundamental matrix found in part (a) to quickly determine the particular solution for the following initial conditions: 이1;8]-[3] x (0) (i) y (0) I (t) =| 3e-5t y (t) = | e2t :8]-[ ] (0): (ii) %3D I (t) = y (t) =

Consider a system of differential equations which has the general solution: :8]-« [}]; 5 e-5+ +C2 C1 (a) Determine the fundamental matrix ¢ (t) which has the property (0) = I. -5t e2t + 8 15 -5t - 15 21 3 8 8 8. * (t) = || 1,2t 8 -5t 5 -5t + 3 2t - (b) Use the fundamental matrix found in part (a) to quickly determine the particular solution for the following initial conditions: 이1;8]-[3] x (0) (i) y (0) I (t) =| 3e-5t y (t) = | e2t :8]-[ ] (0): (ii) %3D I (t) = y (t) =

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

Consider a system of differential equations which has the general solution:
= C1
e-5-t + C2
-1
(a) Determine the fundamental matrix O (t) which has the property (0) = I.
15 2t
8
-5t
15
-5t
8
(t) =
1
12t
-5t
е
+
8
(b) Use the fundamental matrix found in part (a) to quickly determine the particular solution for the following initial conditions:
a (t) = 3e-5t
y (t) =
2t
;8]-[?
x (0)
(ii)
x (t) =
y (t) =

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