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How do you solve the Initial value probelm $dp/dt = 10p(1-p), p(0)=0.1$?

I am reading a proceeding paper where I encountered this differential equation. Can any one kindly write steps of solution (given below) of this equation. $$\frac{\mathrm dI}{\mathrm dt}=aNI(t)-aI^2(t)$$ This first order ordinary differential equation has the following general solution: $$I(t)=\frac N{1+CNe^{-aNt}}$$

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Osman Khalid
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The equation is separable: $$\frac{dI}{NI-I^2} = a\,dt.$$ To solve it, integrate both sides.

Did
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mrf
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  • thank you. Shall I use partial fractions here.. I am sorry, I am kind of stuck. – Osman Khalid Jan 11 '13 at 00:39
  • I solved the above equation using partial fractions. I got the same answer I(t) except that there is no 'N' in the denominator... can any one please confirm. Thanks. – Osman Khalid Jan 11 '13 at 03:04
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    @OsmanKhalid There should be an $N$ in the denominator, i.e. the form given in the question is correct. – mrf Jan 11 '13 at 07:12
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    @OsmanKhalid (But if you like, you can include it in the constant, of course: rename $C$ to $CN$.) – mrf Jan 11 '13 at 07:24
  • Thank you again for reply. So do you mean we can multiply N with constant C. Is it possible in maths? Actually, I am not getting N in denominator... kind of frustrated. Is it possible to provide some hints. Thanks in advance. – Osman Khalid Jan 11 '13 at 22:55
  • Thank you "did" and "mrf". I matched my solution with solution you people referred and got answer of my question. – Osman Khalid Jan 12 '13 at 03:29