# Homework Help: Differential equations hw problem

1. Jan 21, 2010

### gambler84

the rate of growth of the mass M of a spherical rain drop falling through a particular cloud is given by dM/dt = Cr^3 where M = (rho)(4/3)(pi)r^3 and C is a constant

a) eliminate M from the above equation so that the size of the drop is expressed solely in terms of the radius r.

b) separate the variables and integrate to find an expression for r(t), given an intial radius r0 at time t=0

my attempt at part a consisted of me switching the Mass equations to Volume equations, yielding V = (4/3)(pi)r^3
and getting r = (3V/4(pi))^1/3

i dont think this is right. i havent had any differential equations course as of yet

2. Jan 21, 2010

### elibj123

You have M in terms of r. Knowing that r changes in time (dr/dt != 0), what would be dM/dt in terms of r and dr/dt?

3. Jan 21, 2010

### gambler84

idk, thats why i posted the question

4. Jan 21, 2010

### Staff: Mentor

Use the chain rule. You have M = f(r) and f = g(t), so dM/dt = (?)(?)