Differential Equation with growth

[DM1984]

So, I have a differential equation with growth problem. It is a dm/dt function and I need to get it to dD/dt, change in diameter with time.

here is the original functon,
dm/dt= (pi/4)(D)^2* (V(D))*(LWC)*E

E=1
LWC = 2
V(D) = 343D^0.6 m/s

it starts from a diameter of 1mm and grows to 5mm and I need to find the time it takes.

I'm not asking for anyone to solve the problem and give me a final solution, but I need help in getting the dD/dt function.

I thought this was it... but its not:
multiplying by dt ___ dm = [(pi/4)(D)^2 * (v) * (LWC) (E)] dt

integrating ___ m = [(pi/4)(D)^2 * (v) * (LWC) (E)] t

dividing ___ m / [(pi/4)(D)^2 * (v) * (LWC) (E)] = t


thanks

 

[HallsofIvy]

I don't see how you can possibly change from dm/dt to dD/dt without knowing how m is related to D.

 

[DM1984]

m=(pi/6)(density)(D^3)