Show that the function p(t)=1000/(1+99e^-3000x) satisfies the differential equation p' (t)=3p(t)(1000-p(t)) with the initial condition P(0) = 10. I tried it but failed.Please show the full solution.Thanks!

Question

anonymous · Answer

I not sure but what about just take  integral of p'(t)?

anonymous · Answer

You can indeed take the derivative of p(t) and show that p'(t) equals the derivative but I have problem in calculations

anonymous · Answer

Please write te full soluton if you get the answer.I have to go

anonymous · Answer

Well it depends on what easier for you you can also take derivitive of p(t)

anonymous · Answer

p(t)=1000/(1+99e^-3000x)
use chain rule  i thinkfor this one.