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October 6th, 2012, 10:19 AM  #1 
Member Joined: Jul 2010 Posts: 95 Thanks: 0  Differential equation
Hello i need help with this equation: My attempt to solve: AND SO FROM HERE I DON'T KNOW WHAT TO DO ELSE, SO I DID: AND I GOT THE FOLLOWING ; SO I GOT c: MY QUESTION: how to solve this equation? 
October 6th, 2012, 10:36 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Differential equation
You have correctly separated the variables to obtain: Your partial fraction decomposition is incorrect, however. You should find: and so we have: Can you finish? 
October 6th, 2012, 11:25 AM  #3 
Member Joined: Jul 2010 Posts: 95 Thanks: 0  Re: Differential equation
Thanks for your help. I GOT THE FOLLOWING: THEN I TAKE INITIAL CONDITIONS: AND AND THEN: WHAT SHOULD I DO NOW? 
October 6th, 2012, 11:48 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Differential equation
I would write: Convert from logarithmic to exponential form: Using the initial condition: And so we have: 
October 6th, 2012, 12:04 PM  #5 
Member Joined: Jul 2010 Posts: 95 Thanks: 0  Re: Differential equation
Just one stupid question: why Thanks for your help. 
October 6th, 2012, 12:29 PM  #6  
Global Moderator Joined: May 2007 Posts: 6,786 Thanks: 708  Re: Differential equation Quote:
It looks like you made a mistake. Should be:  
October 6th, 2012, 12:31 PM  #7 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Differential equation
There are no stupid questions..."stupid" is not asking when something is not clear. Now, we should observe that is just an arbitrary (positive) constant, so we may write: I should have remarked before, that in the process of separating the variables, the trivial solution was lost. 
October 6th, 2012, 12:33 PM  #8  
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Differential equation Quote:
@OP: So, you need to begin again.  
October 6th, 2012, 03:16 PM  #9 
Member Joined: Jul 2010 Posts: 95 Thanks: 0  Re: Differential equation
Thanks for noticing mistakes and for a very big help. So the last solution i came up is: Given equation: MY ATTEMPT TO SOLVE: AND SO ( and stay the same because they are arbitrary (positive) constant (according to MarkFL)) CONTINUED ( INITIAL VALUES): MY QUESTION: 1. Do I have recalculate c for every given x and y ? 
October 6th, 2012, 10:06 PM  #10  
Senior Member Joined: Aug 2012 From: New Delhi, India Posts: 157 Thanks: 0  Re: Differential equation Quote:
Regards, Rejjy 07Oct2012 11:36 IST  

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