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 February 19th, 2012, 01:48 AM #1 Member   Joined: Jul 2011 Posts: 47 Thanks: 0 Finding the general solution of this differential equation I have the following differential equation: $\frac{dy}{dt}=y(1-y)$ and I need to find the general solution. I end up with: $y(1-y)=e^t$ And from here I can't solve in terms of y (because it's non-linear). How can I proceed?
 February 19th, 2012, 03:28 AM #2 Senior Member   Joined: May 2011 Posts: 501 Thanks: 6 Re: Finding the general solution of this differential equati I think you may have the incorrect set up at the end. Separate variables: $\frac{dy}{y(1-y)}=dt$ Integrate: $\int\frac{dy}{y(1-y)}=\int dt$ $ln\left(\frac{y}{y-1}\right)=t+C$ $\frac{y}{y-1}=e^{t+C}$ Now, you can solve for y.
February 19th, 2012, 03:38 AM   #3
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Re: Finding the general solution of this differential equati

Quote:
 Originally Posted by galactus I think you may have the incorrect set up at the end. Separate variables: $\frac{dy}{y(1-y)}=dt$ Integrate: $\int\frac{dy}{y(1-y)}=\int dt$ $ln\left(\frac{y}{y-1}\right)=t+C$ $\frac{y}{y-1}=e^{t+C}$ Now, you can solve for y.
I figured the following:

$\int\frac{dy}{y(1-y)}=\int\frac{1}{y}+\frac{1}{1-y}$ (I created partial fractions)

Then I integrated them incorrectly (oops) thinking that $\frac{1}{1-y}= log|1-y|$ when it's actually $-log|1-y|$

Thank you very much!

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