We have seen that a system of two linear homogeneous differential equations with constant coefficients can be written in matrix form as x'= Ax. We have also seen that the general solution to such a system can be written as (1) π = c₁k₁e¹₁t + c₂kzełzt where X₁ and X₂ are eigenvalues of A and ₁ and ₂ are corresponding eigenvectors. Solve the system of differential equations below and write your answer in the form of equation (1) above. x': [2² x -1810-181-

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Homework 16:

Question 3

We have seen that a system of two linear homogeneous differential equations with constant
coefficients can be written in matrix form as
x'= Ax.
We have also seen that the general solution to such a system can be written as
(1) x = ₁k₁e¹₁ + ₂kze ¹2t
where A₁ and X₂ are eigenvalues of A and ₁ and ₂ are corresponding eigenvectors.
Solve the system of differential equations below and write your answer in the form of equation (1)
above.
-2 -71
*-[3])
x' =
0
x
-180-180
C1
Transcribed Image Text:We have seen that a system of two linear homogeneous differential equations with constant coefficients can be written in matrix form as x'= Ax. We have also seen that the general solution to such a system can be written as (1) x = ₁k₁e¹₁ + ₂kze ¹2t where A₁ and X₂ are eigenvalues of A and ₁ and ₂ are corresponding eigenvectors. Solve the system of differential equations below and write your answer in the form of equation (1) above. -2 -71 *-[3]) x' = 0 x -180-180 C1
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