The system tx_ = Ax is analogous to the second-order Euler equation (Section 5.4)

Chapter 7, Problem 13

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QUESTION:

The system tx_ = Ax is analogous to the second-order Euler equation (Section 5.4). Assuming that x = tr , where is a constant vector, show that and r must satisfy (ArI) = 0 in order to obtain nontrivial solutions of the given differential equation. Referring to 13, solve the given system of equations in each of 14 through 16. Assume that t > 0. 1

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QUESTION:

The system tx_ = Ax is analogous to the second-order Euler equation (Section 5.4). Assuming that x = tr , where is a constant vector, show that and r must satisfy (ArI) = 0 in order to obtain nontrivial solutions of the given differential equation. Referring to 13, solve the given system of equations in each of 14 through 16. Assume that t > 0. 1

ANSWER:

Step 1 of 2

If  is a solution, then it must satisfy the differential equation .

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