Ch07_2HWsoln - Solutions for Exercise Set 2 1 Verify that the following function solves the given system of DEs 1 2 x(t = C1 et 2 1 C2 e2t 3 2 2 2 x= x

Ch07_2HWsoln - Solutions for Exercise Set 2 1 Verify that...

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Solutions for Exercise Set 2 1. Verify that the following function solves the given system of DEs:x(t) =C1e-t12+C2e2t21x0=3-22-2xSOLUTION: First, we computex0, then we’ll compare it toAx:Forx0, we have-C1e-t12+ 2C2e2t21ForAx, we have:C1e-t3-22-212+C2e2t3-22-221=C1e-t-1-2+C2e2t42=-C1e-t12+ 2C2e2t212. Convert each of the systemsx0=Axinto a single second order dif-ferential equation, and solve it using methods from Chapter 3, ifAisgiven below:(a)A=12-5-1 1

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