3. Solve the following: (1 -1 -1 (a) X' =| 1 3 1 X 0 0 2 (1 2 -3) (b) X' = | 1 1 2 X 1 -1 4

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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1. Convert the following system of first order differential equations with initial condition into I.V.P and
solve both of them:
(2t - 2t-2
X1
(t) =
X1
X1
(1)
2. Let X" (t) =
X (t) =
2t
be solutions of X'(t) = P(t)X
(a) Find W(X" (t), X® (t)).
(b) In any intervals x®(t), X (t) are linearly independent?
(c)Find P(t).
(d) Find the general solution of X'(t) = P(t)X fort + 0.
3. Solve the following:
(1 -1 -1
(a) X' =| 1
3
1 X
2
(1 2
-3
2 X
(b) X' =|1
(1
1
-1
4
(2 0
(c) X' = 1
2
1 X
1
-1 2
Transcribed Image Text:1. Convert the following system of first order differential equations with initial condition into I.V.P and solve both of them: (2t - 2t-2 X1 (t) = X1 X1 (1) 2. Let X" (t) = X (t) = 2t be solutions of X'(t) = P(t)X (a) Find W(X" (t), X® (t)). (b) In any intervals x®(t), X (t) are linearly independent? (c)Find P(t). (d) Find the general solution of X'(t) = P(t)X fort + 0. 3. Solve the following: (1 -1 -1 (a) X' =| 1 3 1 X 2 (1 2 -3 2 X (b) X' =|1 (1 1 -1 4 (2 0 (c) X' = 1 2 1 X 1 -1 2
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