2. Find the general solution of the system of differen- tial equations d '( cos(3t) - sin(3t) 9 3 sin(3t) cos(3t) dt x+ 2tet + 4t³et -3 9 Hint: The characteristic polynomial of the coefficient matrix is (A – 9)² + 3².

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A: We will convert the given system to a system of first order differential equations in matrix form.

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Q: 3. Find the general solution of the system of differential equations d X = dt 8 -5 X 10 cos(7t) – 7…

A: Given: ddt(x)=8-5106x+4t3e7tcos(7t)-7sin(7t)10cos(7t)+8t7e7t7cos(7t)-sin(7t)10sin(7t) Here A=8-5106

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A: Given: R1= 8 R2=3 L1=1 L2=1

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Q: 2.2 The currents x and y in a coupled circuit are modeled by the system: dx = x - 2y dt dy = 2x + y…

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Q: 2. Find the general solution of the system of differen- tial equations d X = dt + 4t³e4 / sin(3t)…

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Q: Еxercise 4 : Let the following homogeneous linear system dr dt = x – y + 3z (c) 4 = 2y – 2z 器= 32 ai…

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Q: 5. Find the general solution of the system of differential equations 2 d -2 11 7 х. dt -7 -3 Hint:…

A: We solve the given system of differential equations by finding eigenvalues and corresponding…

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A: please see the next step for solution

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Q: 3. Find the general solution of the system of differential equations d X = dt 8. -5 10 cos(7t) – 7…

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Q: 4. Find the general solution of the system of differential equations 15 8 -4 d. 4 11 4 x+ 14 X%3D dt…

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Q: 1)Using the Jordan Real Canonical Form, find the solution to the initial value problem Ar 피(0) where…

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Q: Solve the initial value problem for the linear system æ' = Ax in dimension 3, where 7 -1 -1 A = |1 5…

A: To solve the initial value problem

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A: Note: According to bartleby guidelines; for more than one question asked, only the first one is to…

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A: The solution is given as follows

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Q: 4. Find the general solution of the system of differential equations 15 8 -4 5 d. 4 11 4 x + 14 dt 4…

A: We will use standard technique

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Q: 7. Consider the normal noninvertible 3 x 3 matrix 0 10 1 0 1 0 1 0 A = (i) Find the spectral…

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Q: What are the roots of the characteristic equation of the following system dz -2z + 2y-3z dt dy…

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Q: What are the roots of the characteristic equation of the following system? dr dt dy -+2y+z dt dz 3y+…

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Q: (b) Compute el for 1 -1 1 Solve the following linear nonhomogeneous system: x = x1 – x2 + 4 x½ = x1+…

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Q: 1. Find the general solution of the system of differential equations 9 -4 х. d X = dt 5 5 Hint: The…

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A: NOTE. Answer form may vary depending upon choice of eigen vector.

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Q: 10

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Q: 10. Find the general solution of the system of differential equations d 3 -2 -2 -3 -2 -6 dt 10 2 2 1…

A: Given system of differential equation is ddtx=3-2-2-3-2-63610x+2te4t2-10+3t2e4t20-1+4t3e3t13-3…

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Q: Use the results of LU decomposition 1 2 -3 -1 A=LU=|3/2 l1/2 1 0 1/2 -1/2| 1 1] Lo 1 to solve Ax=b,…

A: Consider the matrix: A=100321012112-3-1012-12001……1bT=1-11……2   Also, AX=b……3

Q: 9

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Q: 3. Find the general solution of the system of differen- tial equations d 12 -4 X = dt 2 8 + 2te10t…

A: Given, ddtx=12-428x+2te10tcos2t-sin2tcos2t+4t3e10tcos2t+sin2tsin2t...1 And the given characteristics…

Q: Consider a system of differential equations X Ax, where x = and the 2x2 matrix A has eigenpairs d1 =…

A: To find the given options