1. A spherical raindrop evaporates at a rate proportional to its surface area. Write a
dierential equation (with a constant of proportionality k) for the volume of the raindrop
as a function of time.
1. Find the value of A for which the solution of the initial value problem
y y = 1 + 3 sin t,
y(0) = A
remains nite as t .
Answer : We have et as an integrating factor, and multiplication by the integrating factor yield