Find a fundamental matrix of the following system, and then apply x(t)=(t)(0) 1x to find a solution satisfying the initial conditions. -6-2 x' = x, x(0)= 36 6 1+2t - 6-2 e-6t| 2 cos 6t - 2 sin 6t C. (t)= - 6 cos 6t + 6 sin 6t 6 cos 6t + 6 sin 6t - 6t - 2e - 6t OD. (t)= 6e -2 e 6t -6t 6e Find a solution satisfying the given initial condition. x(t) = (Use integers or fractions for any numbers in the expression.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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Find a fundamental matrix of the following system, and then apply x(t) = (t)Þ(0) 1x to find a solution satisfying the initial
conditions.
-6-2
x' =
X, X(0)=
(0)-[1]
36
G
1+2t - 6-2 e-6
2 cos 6t
- 2 sin 6t
C. (t)=
- 6 cos 6t + 6 sin 6t 6 cos 6t + 6 sin 6t
6e - 6t
-2 e-6t
D. Φ(t) =
-2e
, 6t
6 e-6t
Find a solution satisfying the given initial condition.
x(t) = ¯
(Use integers or fractions for any numbers in the expression.)
Transcribed Image Text:Find a fundamental matrix of the following system, and then apply x(t) = (t)Þ(0) 1x to find a solution satisfying the initial conditions. -6-2 x' = X, X(0)= (0)-[1] 36 G 1+2t - 6-2 e-6 2 cos 6t - 2 sin 6t C. (t)= - 6 cos 6t + 6 sin 6t 6 cos 6t + 6 sin 6t 6e - 6t -2 e-6t D. Φ(t) = -2e , 6t 6 e-6t Find a solution satisfying the given initial condition. x(t) = ¯ (Use integers or fractions for any numbers in the expression.)
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