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Differential Equation with growth 
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#1
Nov1212, 07:52 PM

P: 6

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 


#2
Nov1312, 07:53 AM

Math
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Thanks
PF Gold
P: 39,571

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



#3
Nov1312, 09:06 AM

P: 6

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



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