Page 356 - Schaum's Outline of Differential Equations
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ANSWERS TO SUPPLEMENTARY   PROBLEMS                        339




                                  boundary conditions  1.49.  No values; boundary conditions

         1.50.  d  = -2, c 2 = 3                     1.51.  d  = 0, c 2 = 1

         1.52.  d  = 3, c 2 = -6                     1.53.  c 1 = 0, c 2 = 1







         CHAPTER 2





         2.13.  Ine  volume  and  the  temperature  are  in  direct  proportion.  As  one  increases,  so  will  the  other;  as  one  decreases,
              so will the other.

         2.14.  The net force acting on a body is proportional the body's  acceleration.  This assumes  the mass is constant.

         2.15.  Since  t is increasing,  and  T(576)  = 0, this model  is valid for  576  hours. Any  time afterwards  gives us  a negative
              radicand,  and hence,  an imaginary answer,  thereby rendering the model  useless.

         2.16.  At t = 10, because 7"(10) = 0, and T'(t) >0fott>  10.

         2.17.  The motion must be periodic,  because sin 2t is a periodic function of period  n.

         2.18.  (a)  2 cos 2t;  (b)  -4 sin 2t
         2.19.  (a)  y  is a constant;  (b)  y  is increasing;  (c)  y  is decreasing;  (d)  y  is increasing.

                         3
         2.20.  —  = k(M  -  X ) ,  where k is a negative constant.
               dt
         2.21.  The  rates  of change  of  gallons of liquid sugar per hour.

         2.22.  The rates of change of the vats (gal/hr) are affected by the amount of liquid sugar present in the vats, as the equations
              reflect.  The  signs and magnitudes of the constants  (a, b, c, d, e, and/) will determine whether  there is an  increase
              or decrease of sugar, depending on the time. The units for a, b, c, and d is (1/hr); the units for e and/is (gal/hr).




         CHAPTER 3

                                                                 x
                   2
         3.15.  y' = -y lx                           3.16.  y' = xl(e - 1)
                        2
         3.17.  / = (sin;t-;y -;y) 1/3               3.18.  Cannot  reduce  to standard form
         3.19.  y' = -y + lnx                        3.20.  / = 2 and / = x + y + 3




                                                                 x
                                                     3.24.  y' = ye- -e x
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