Question: Help with this question? Consider the IVP uj = 3u1, U2 = u1 + 2u2, with initial conditions specified at time t = 0. (a)

Help with this question?

Consider the IVP uj = 3u1, U2 = u1 + 2u2, with initial conditions specified at time t = 0. (a) Determine the Lipschitz constant for this system in the max-norm || . | and the 1-norm || . I/1. (See Appendix A.3.) (b) Solve this problem in two different ways: i. Solve the first equation, which only involves u1, and then insert this function into the second equation to obtain a nonhomogeneous linear equation for u2. Solve this using (5.8). ii. Write the system as u' = Au and compute the matrix exponential using (D.35) to obtain the solution. (See Appendix C.3 for a discussion of the Jordan Canonical form in the defective case.)

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