√1000以上 ƒƒ“ƒY ”¯Œ^ ƒVƒ‡[ƒg ƒc[ƒuƒƒbƒN 30‘ã 289013

Math 54 Selected Solutions for Week 5 Section 42 (Page 194) 28 Consider the following two systems of equations 5x 1 x 2 3x 3 = 0 9x 1 2x 2 5x 3 = 1 4x 1 x 2 6x 3 = 9 5x 1 x 2 3x 3 = 0 9x 1 2x 2 5x 3 = 5 4x 1 x 2 6x 3 = 45 It can be shown that the rst system has a solution

ƒƒ“ƒY ”¯Œ^ ƒVƒ‡[ƒg ƒc[ƒuƒƒbƒN 30‘ã-G B c , P b R a c Lab a , NIOSH J B , Occ a a Sa a H a A aExample 112 Verify that the family of solutions v = gt C for y0= g is the general solution SOLUTION Let y 0(t) = gt If y 1(t) is another solution of the differential equation, then y0 1 (t) = y0 0 (t) = g It follows from theequal derivatives theoremthat y 1(t) y 0(t)C In other words, every solution of theODE belongs to the family y

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