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 October 6th, 2012, 11:23 PM #11 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs Re: Differential equation In the process of separating the variables, we divided by $y^2+2y$ which means $y\ne0$, yet $y=0$ satisfies the ODE (as you can see) as what is called a trivial solution, and we lose this in the process.
 October 6th, 2012, 11:37 PM #12 Senior Member   Joined: Aug 2012 From: New Delhi, India Posts: 157 Thanks: 0 Re: Differential equation How does it satisfy the ODE? You just get $y'=0$ Does that mean it is a solution?
 October 6th, 2012, 11:39 PM #13 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs Re: Differential equation If $y=0$ then $y'=0$ as well.

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