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November 8th, 2016, 09:04 AM   #1
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First order differential equation

Hey all, I have a separable differential equation:

Can someone please explain how the solution is:


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November 8th, 2016, 09:25 AM   #2
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Post your attempt first. There's nothing that should cause a differential equations student much trouble, especially if you know how to integrate by partial fractions (writing your constant of integration as $\ln c$) and how to use logarithmic identities to good effect.

Perhaps the hardest part is removing the absolute value signs.
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November 8th, 2016, 11:09 AM   #3
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I get 1/2ln(2x+1)=ln(t/(t+1))+ln(C), but what should I do then?

Last edited by skipjack; November 8th, 2016 at 02:49 PM. Reason: to insert parentheses
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November 8th, 2016, 02:54 PM   #4
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Can you write that equation in the form ln(...) = ln(...)?
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November 8th, 2016, 03:38 PM   #5
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You are looking for the terms in $t$ to be squared, so multiply by 2 and use properties of the logarithm.

Last edited by skipjack; November 8th, 2016 at 03:41 PM.
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November 8th, 2016, 03:42 PM   #6
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Mrkukas, are you given that t > 0?
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November 8th, 2016, 04:42 PM   #7
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He shouldn't be. It should be a valid result for all $t$ with the possible exception of $t=-1$.
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November 8th, 2016, 06:16 PM   #8
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That depends on what you mean by "valid result" and "possible exception".

The original equation doesn't imply that t isn't -1, but the supplied solution does, as it's undefined at t = -1.
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November 8th, 2016, 11:34 PM   #9
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Quote:
Originally Posted by skipjack View Post
Mrkukas, are you given that t > 0?
No, I am not.

Last edited by skipjack; November 8th, 2016 at 11:51 PM.
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November 8th, 2016, 11:53 PM   #10
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Can you assume that t is real?
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