AB 5. (a) The differential equation is separable:
If y = 0 when x = 2, then thus c = 3, and
Solving for y gives the solution:
Note that is defined only if
only if the numerator and denominator have the same sign.Since the particular solution must be continuous on an interval containing the initial point x
= 2, the domain is (Review Chapter 9)
(b) Since the function has a horizontal asymptote at y = ln 3.
(Review Chapter 2)