Find a general solution of the linear system below. x'= - 12x + 4y, y'' = 3x - 13y Solve for x(t). Choose the correct answer below. A. x(t) = C₁ cos 3t + C₂ sin 3t+ c3 cos 4t + c4 sin 4t B. X(t) = C₁ cos 9t + c2 sin 9t + c3 cos 16t + c4 sin 16t C. X(t)=C₁e 16t 9t + Cze D. x(t) = C₁ e - 9t - 3t + C₂ + 3t + C3 16t - 4t +C4e + C4e4t Now find y(t) so that y(t) and the solution for x(t) found in the previous step are a general solution to the system of differential equations. y(t) =

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter1: Systems Of Linear Equations
Section1.1: Introduction To Systems Of Linear Equations
Problem 90E: Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the...
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Find a general solution of the linear system below.
x'' = 12x + 4y, y'' = 3x - 13y
Solve for x(t). Choose the correct answer below.
A. x(t) = C₁ cos 3t + c₂ sin 3t + c3 cos 4t + C4
B. X(t) = C₁ cos 9t + c2 sin 9t + c3 cos 16t + c4 sin 16t
- 16t+C4e
C.
- 9t
x(t) = C₁ e +
D. x(t)=c₁e 3t
e⁹t
- C၇e
3t
+C₂e
+ C3e
+ c3e
4t
+
16t
sin 4t
C4e4t
Now find y(t) so that y(t) and the solution for x(t) found in the previous step are a general solution to the system of
differential equations.
y(t) =
Transcribed Image Text:Find a general solution of the linear system below. x'' = 12x + 4y, y'' = 3x - 13y Solve for x(t). Choose the correct answer below. A. x(t) = C₁ cos 3t + c₂ sin 3t + c3 cos 4t + C4 B. X(t) = C₁ cos 9t + c2 sin 9t + c3 cos 16t + c4 sin 16t - 16t+C4e C. - 9t x(t) = C₁ e + D. x(t)=c₁e 3t e⁹t - C၇e 3t +C₂e + C3e + c3e 4t + 16t sin 4t C4e4t Now find y(t) so that y(t) and the solution for x(t) found in the previous step are a general solution to the system of differential equations. y(t) =
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