Good afternoon folks. I am getting ready to start a Planetary Physics course next week and have been doing some of the old homework that is posted on the course site. I am struggling to figure this one out and would love some help. It's been about 5 years since first year calculus, so I am a little lost. Any guidance would be greatly appreciated. 1. The problem statement, all variables and given/known data 1. In class, we saw that the rate of growth of a planet can be written as dM/dt = rsvR2(1+(8GrR2/v2) (1) where M is the mass, t is time, r and rs are the densities of the solid planet and the planetesimal swarm, G is the gravitational constant, R is the planet radius and v is the relative velocity. b) Using the relationship between mass and density for a solid body and the chain rule, rewrite equation (1) in terms of dR/dt. (1) 2. Equations As far as any working equations for this, I assumed that we should use the fact that density = mass/volume. Since we assume the vacuum of space, the solid body would be spherical (or nearly so), thus volume could be substituted for 4/3 pir3 giving us the (useful???) equation to substitute in for both the swarm density and the density of the object density = (3m)/(4pir3) Your answer to part b) is a first-order differential equation, but it’s non-linear, so it’s hard to solve completely. it has been quite some time since i've worked with an equation like this in the fashion mentioned, so I am just struggling to make any headway. Any explanations would be very helpful.