Let x(t) = x₁ (t) x'₂ (t) = If x (0) [ x₂(t): = x₁(t) x₂ (t) be a solution to the system of differential equations: 5 B 5 Put the eigenvalues in ascending order when you enter x1(t), 2 (t) below. x₁(t): Jexp(t)+ Jexp(t)+ 4x₁(t) + 2x₂ (t) -3x1(t) + 9x2(t) find x (t). exp([ exp(t) exp(t)

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A: Given differential equation y'''=2y''+9y'+6y y'→=Ay→y→=yy'y''

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Q: 0 -2 has characteristic equation The matrix A det [0 -> a11 a12 = = a21 a22 1 -2 -2 = 1 -2-X…

A: Step 1:

Q: Suppose that the differential equation x' = Ax is such that A is a 2 × 2 matrix with eigenvalues A1…

A: See the detailed solution below.

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Q: Solve the system of differential equations x' = 3x + Oy y' = 12x + ly - 2 (0) %3 3, у(0) 3D 10

A: given difference equation x'=3x+0yy'=-12x+y with initial condition x0=3 , y0=10

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A: Here we will evaluate each value.

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Q: 7- Write the differential equation y"(t) - 2y"(t)- y'(t) + 3y(t) = 0 as a first order system. [x'…

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Q: Solve the second order differential equation ý + ý - 6y = 8e* + 3x A:y = ce2x + cze-3x + 2e* + %3D 2…

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Q: Q1) Solve and plot the following system of ordinary differential equations: x'(t) = x(t)-2y(t) +…

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Q: Suppose 3/₁ Y/2 = = This system of linear differential equations can be put in the form y' = P(t)y +…

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Q: 1. (a) What are A, x' and x'' in matrix form X'= AX of the system of differential equations ($) x₁ =…

A: First we find the general form of the system and then find the eigen values and eigen vectors of the…