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Get Full Access to Elementary Differential Equations And Boundary Value Problems - 10 Edition - Chapter 2.1 - Problem 38
Get Full Access to Elementary Differential Equations And Boundary Value Problems - 10 Edition - Chapter 2.1 - Problem 38

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# Variation of Parameters. Consider the following method of ISBN: 9780470458310 168

## Solution for problem 38 Chapter 2.1

Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Problem 38

Variation of Parameters. Consider the following method of solving the general linearequation of first order:y+ p(t)y = g(t). (i)(a) If g(t) = 0 for all t, show that the solution isy = A exp p(t) dt, (ii)where A is a constant.(b) If g(t) is not everywhere zero, assume that the solution of Eq. (i) is of the formy = A(t) exp p(t) dt, where A is now a function of t. By substituting for y in the given differential equation,show that A(t) must satisfy the conditionA(t) = g(t) exp p(t) dt. (iv)(c) Find A(t) from Eq. (iv). Then substitute for A(t) in Eq. (iii) and determine y. Verifythat the solution obtained in this manner agrees with that of Eq. (33) in the text. Thistechnique is known as the method of variation of parameters; it is discussed in detail inSection 3.6 in connection with second order linear equations.

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Section 1.2 Gauss-Jordan Elimination There are three legal elementary row operations: (1) Multiply a row by a nonzero constant. Example: 2R 1 would multiply every entry in the first row of a matrix by 2. (2) Switch two rows. R ↔ R Example: 1 2 would interchange the elements in the first and second rows. (3) Add a multiple of one row to another. R + 2R Example: 1 2 would add twice the elements in the second row to the elements in the first row. Note that whatever is written first is what changes. Gauss-Jordan Elimination is made up of any combination of these row 10 a  operations. Our goal is to get 1 b  0 x 010 y or    1 z Example: Use Gauss-Jordan

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##### ISBN: 9780470458310

This textbook survival guide was created for the textbook: Elementary Differential Equations and Boundary Value Problems, edition: 10. Since the solution to 38 from 2.1 chapter was answered, more than 235 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 76 chapters, and 2039 solutions. The answer to “Variation of Parameters. Consider the following method of solving the general linearequation of first order:y+ p(t)y = g(t). (i)(a) If g(t) = 0 for all t, show that the solution isy = A exp p(t) dt, (ii)where A is a constant.(b) If g(t) is not everywhere zero, assume that the solution of Eq. (i) is of the formy = A(t) exp p(t) dt, where A is now a function of t. By substituting for y in the given differential equation,show that A(t) must satisfy the conditionA(t) = g(t) exp p(t) dt. (iv)(c) Find A(t) from Eq. (iv). Then substitute for A(t) in Eq. (iii) and determine y. Verifythat the solution obtained in this manner agrees with that of Eq. (33) in the text. Thistechnique is known as the method of variation of parameters; it is discussed in detail inSection 3.6 in connection with second order linear equations.” is broken down into a number of easy to follow steps, and 147 words. The full step-by-step solution to problem: 38 from chapter: 2.1 was answered by , our top Math solution expert on 12/23/17, 04:36PM. Elementary Differential Equations and Boundary Value Problems was written by and is associated to the ISBN: 9780470458310.

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