Exercise 1.3.5 For each of the following homogeneous systems, find a set of basic solutions and express the gen- eral solution as a linear combination of these basic solu- tions. a. x12x2 x3 + 2x4 +x5=0 b. C. - x1 + 2x2 + 2x3 +x5=0 2x1 + 4x2 - 2x3 + 3x4+x5=0 x1+2x2 X3 X4 X5 = 0 - -x1-2x2+2x3 + x5=0 -x12x2+3x3 + x4+3x5=0 - x1 + x2 x3 + 2x4 + x1 + 2x2 x3 + x4+ - x5=0 x5 = 0 2x13x2 x3 + 2x4 + x5=0 - 4x1+5x22x3 + 5x4 + 2x5 = 0

Exercise 1.3.5 For each of the following homogeneous systems, find a set of basic solutions and express the gen- eral solution as a linear combination of these basic solu- tions. a. x12x2 x3 + 2x4 +x5=0 b. C. - x1 + 2x2 + 2x3 +x5=0 2x1 + 4x2 - 2x3 + 3x4+x5=0 x1+2x2 X3 X4 X5 = 0 - -x1-2x2+2x3 + x5=0 -x12x2+3x3 + x4+3x5=0 - x1 + x2 x3 + 2x4 + x1 + 2x2 x3 + x4+ - x5=0 x5 = 0 2x13x2 x3 + 2x4 + x5=0 - 4x1+5x22x3 + 5x4 + 2x5 = 0

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.6: Applications Of Differential Equations

Problem 15E: Solve Exercise 14 if a 25 solution of the same mixture is added instead of pure alcohol.

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