5) Given the following homogeneous system of first-order differential linear equations. dx dt =-6x+ Gx+2y dy= = = 3x + y Dr X²=> [si] X a) Find the 2 eigenvalues .62 31 b) Find the 2 corresponding eigenvectors c) Find the 2 special vector Solutions d) show that the 2 special Vector solutions are linearly independent e) Write out the general solution System f) Find a specific solution of the System for X (0) = 100)] = [ Lycos]= of the

Q: answers should be separated by comma and in general solution form

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Q: What is the real form of the general solution of the second order, linear, homogeneous differential…

A: Given eigen value λ1 =-2+iλ2=-2-iCorresponding Auxiliary equation:-m2-( λ1+…

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Q: Give the General Solution.  (d/dt)(vector(x)) = matrix(2,3,-3,2)vector(x)

A: Given that,  ddtx1x2=23-32x1x2 The corresponding linear equations are, x1'=2x1+3x2x2'=-3x1+2x2…

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Q: 39 2-31]2, 2004] 니 dz de where 2 =/ 2₁1 and 12 = [ 2.1 2-√² ] Z

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Q: Verify that the vector X is a solution of the given homogeneous system. -1 X' = 4 X; x = -3t/2 1 (*)…

A: Given the homogeneous system is x'=-1141-1x x=-12e-3t2

Q: 2) Find the General Solution of the System of Equations. 1 0 X' =|2 1 - 2 X 3 2 1

A: Given: X'=10021-2321X

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A: We will use the following Newton-Rapson formula for finding the roots of 2 variable equations.…

Q: a 14. If the complex number 3i is an eigenvalue of a matrix A = (d) a, b, c, d are real numbers,…

A: Solution:Given that, matrix  and the eigenvalue of the matrix A is 3i.

Q: 1. Solve the system of linear differential equations: x₁ = 3x₁ + x₂ x₂ = −2x₁2x₂ + x3 x3 = -2x₂ +…

A: x1'=3x1+x2x2'=-2x1-2x2+x3x3'=-2x2+3x3

Q: x' = 14x + 24y y' = - 8x + 14y x(0) = 1, y(0) = 0

A: NOTE: Refresh your page if you can't see any equations. . take determinan=0…

Q: Consider the dynamical system Vk+1 = AVk where  V0 =  0 3 A= 0 1 6 -1   Find a formula in terms…

A: The given dynamical system is Vk+1=AVk, where V0=03, A=016-1. The objective is to calculate the…

Q: Consider a system of two linear first-order ordinary differential equations: Y₁ = Y1 — Y2, _Y2 = 2y1…

A: Given system of differential equationsy˙1=y1−y2y˙2=2y1−y2In Matrix form [y˙1y˙2]=[1−12−1][y1y2]Let…

Q: Edit t2 Consider the vectors x(t) = ) and x (t) 6. 4t (a) Compute the Wronskian of x) and x(2). W =…

A: We have to find P(t) such that X'=P(t)X.

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Q: Let in = be the solution to the discrete dynamical system Yn Xn+1 6xn – 13yn - Yn+1 = 0xn - [:] -3…

A: Given that, xn+1=6xn-13yn             (1)yn+1=0xn-7yn               (2) and  v0→=-3-1, i.e⇒x0=-3,…