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October 6th, 2012, 10:19 AM   #1
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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?
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October 6th, 2012, 10:36 AM   #2
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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?
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October 6th, 2012, 11:25 AM   #3
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Re: Differential equation

Thanks for your help.



I GOT THE FOLLOWING:







THEN I TAKE INITIAL CONDITIONS:



AND






AND THEN:





WHAT SHOULD I DO NOW?
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October 6th, 2012, 11:48 AM   #4
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Re: Differential equation

I would write:



Convert from logarithmic to exponential form:



Using the initial condition:







And so we have:







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October 6th, 2012, 12:04 PM   #5
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Re: Differential equation

Just one stupid question:

why



Thanks for your help.
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October 6th, 2012, 12:29 PM   #6
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Re: Differential equation

Quote:
Originally Posted by safyras
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?


It looks like you made a mistake. Should be:
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October 6th, 2012, 12:31 PM   #7
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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.
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October 6th, 2012, 12:33 PM   #8
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Re: Differential equation

Quote:
Originally Posted by mathman
...It looks like you made a mistake...
Geez...you are right.

@OP: So, you need to begin again.
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October 6th, 2012, 03:16 PM   #9
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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 ?
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October 6th, 2012, 10:06 PM   #10
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Re: Differential equation

Quote:
Originally Posted by MarkFL
.....
I should have remarked before, that in the process of separating the variables, the trivial solution was lost.
What do you mean by this?
Regards,
Rejjy
07-Oct-2012
11:36 IST
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