3. (5 s) Reduce the given third order differential equation to a system of first order equations. Then write the system of equations in matrix form of the form x' = Ax+ f where A is a 3 × 3 matrix, x is a 3 × 1 vector and f is a 3 × 1 vector. y"" +3ty" +3ty' + y = 7

Q: - (4y" + fy) = -A with y(-1) = -2, y(-1) = 1, y"(-1) = 0 Use x1 = y, x2 = y', and x3 = y". x + with…

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Q: λ1 = -2, λ2=5  V1 = (1, -2)  V2 = (4, -1) Using the above eigenvalues and/or eigenvectors, find…

A: I have used eigenvalue and eigenvector method to solve the given system of ODE.

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A: See the details solution below

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A: The given second order equation is 2y''+4y'+6y=cost  …(1) To convert into 1st order system of…

Q: Solve the system Ÿ' = AŸ + Ġ for A

A: a0 A = 7-143 , B = 5505 , P = 122-1Then p-1 = 1-1 -4 -1-2-21               = 1-5 -1-2-21…

Q: Find the general solution of the given system of equations. Solve using similarit transforms. x' =…

A: Given,           x'=2-13-2x+1-1et

Q: Z₁' (t) = -6₁2 + 1.12₁ -0.822 Z₂²' (t) = -13.8 +2.12, -1.222 Z₁ (0) =11 Z₂₁₂ (0) = 4

A: The given system of differential equations are as follows.Find the equalibrium point as follows.Put…

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Q: Transform the given differential equation or system into an equivalent system of first-order…

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Q: Equations (1.1) and (1.2) are linear differential equations for a drug delivery system. + 5x -y = 0…

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Q: Convert the differential equation u"+2u'+5ue into a system of first order equations by letting x =…

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Q: 3 ve the nonhomogeneous system tY' = (²2 =²) x + (-²₁) -21). Y (2-2)

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Q: Convert the differential equation u"-3u-2u: = est into a system of first order equations by letting…

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Q: Q9. Solve the system of differential equations = () 3 Y' = AY, Y (0) = ( where A = () :). -1 1 %3|…

A: Determine eigenvalues of A:…

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Q: For the system of differential equations do the following. n' = n(1-2m), m' = m(2 - 2n - m), n, m≥ 0

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Q: x' = 4x + y + 2t, y' = −2x + y

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Q: λ1 = -2, λ2=5  V1 = (1, -2)  V2 = (4, -1) Using the above eigenvalues and/or eigenvectors, find…

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Q: Given the System of Differential Equations x' + 5x = 6y y' - 8y = 1 1x Rewrite the System as a…

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