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

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

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Extra info for Elementary Diff Eqns and Boundary-Value Problems

Example text

The partial derivative `0 Î`C œ -9>a>bÎa"  C b# has the same region of continuity. 14. > Þ Integrating both sides, the solution is given by Ca>b œ C! ÎÐ"  C! ># ÑÞ For C!  ! , solutions exist as long as >#  "ÎC! For C! Ÿ ! , solutions are defined for all > . 15. > Þ Integrating both sides and invoking the initial condition, Ca>b œ C! ÎÈ#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 !

The differential equation is separable, with ________________________________________________________________________ page 46 —————————————————————————— CHAPTER 2. —— Ba@b œ  7@ 7# 1 71  5 @  # 68º ºÞ 5 5 71 The inverse exists, since both B and @ are monotone increasing. b œ "$Þ%& meters . Þ#% . a- bÞ In parta+b, set @ œ "! m/s and B œ "! meters . 29a+bÞ Let B represent the height above the earth's surface. > œ  K aVBb# , in which K is the universal gravitational constant. The symbols Q and V are the mass and radius of the earth, respectively.

The solution may also be expressed as W a>b œ ÐW!  5< Ñ/<>  5< Þ Note that if the withdrawal rate is 5! œ < W! , the balance will remain at a constant level W! Þ 5 a- b. Assuming that 5  5! , W aX! b œ ! for X! œ "< 68’ 55 “Þ ! a. 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 ("& .

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