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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 which means , yet 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 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 then as well.


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