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