Elementary Diff Eqns and Boundary-Value Problems - download pdf or read online

By W. Boyce, R. DiPrima [SOLUTIONS MANUAL]

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Extra info for Elementary Diff Eqns and Boundary-Value Problems

Example text

C! >  " Þ Solutions exist as long as #C! >  "  ! , that is, #C! >   " . If C!  ! , solutions exist for >   "Î#C! If C! œ ! , then the solution Ca>b œ ! exists for all > . If C!  ! , solutions exist for >   "Î#C! 16. The function 0 a> ß C b is discontinuous along the straight lines > œ  " and C œ ! The partial derivative `0 Î`C is discontinuous along the same lines. The equation is ________________________________________________________________________ page 49 —————————————————————————— CHAPTER 2.

B. ) and 5 œ #5! , then X! œ )Þ'' years . a/b. Setting W a>b œ ! and solving for /<> in Parta,b, /<> œ results in 5 œ œ X a0 bÞ In parta/b, let 5 œ "#ß !!! ) , and X œ #! The required investment becomes W! œ $ ""*ß ("& . 14a+bÞ Let U w œ  < U Þ The general solution is Ua>b œ U! /<> Þ Based on the definition of half-life, consider the equation U! Î# œ U! /&($! < Þ It follows that ________________________________________________________________________ page 41 —————————————————————————— CHAPTER 2.

W aD b œ V aD bÞ The latter equation is separable, with . D Þ Therefore, given V œ V aBC b, it is possible to determine . aBC b which becomes an integrating factor of the differential equation. ________________________________________________________________________ page 61 —————————————————————————— CHAPTER 2. —— 28. The equation is not exact, since RB  QC œ #C  " . However, aRB  QC bÎQ œ œ a#C  "bÎC is a function of C alone. Hence there exists . w œ a#  "ÎCb. The latter equation is separable, with .

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Elementary Diff Eqns and Boundary-Value Problems by W. Boyce, R. DiPrima [SOLUTIONS MANUAL]

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