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 Post subject: separation of variables involving a quadraticPosted: Tue, 7 Aug 2012 21:53:01 UTC
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Joined: Thu, 2 Apr 2009 04:25:13 UTC
Posts: 91
given problem:

dx/dt=k(3-x)(2-x)

x(0)=1

I have a worked solution for this problem and it uses partial fractions as a key method.

My question is whether this problem can be solved without partial fractions, ie: combining terms to produce a quadratic in x.

A yes or no is what I am looking for. If yes I will attempt to work the problem.

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 Post subject: Re: separation of variables involving a quadraticPosted: Wed, 8 Aug 2012 03:09:44 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6007
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
given problem:

dx/dt=k(3-x)(2-x)

x(0)=1

I have a worked solution for this problem and it uses partial fractions as a key method.

My question is whether this problem can be solved without partial fractions, ie: combining terms to produce a quadratic in x.

A yes or no is what I am looking for. If yes I will attempt to work the problem.

Recall .

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 Post subject: Re: separation of variables involving a quadraticPosted: Wed, 12 Sep 2012 01:36:18 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7949
Location: Lexington, MA

Quote:

I have a worked solution for this problem and it uses partial fractions as a key method.

My question is whether this problem can be solved without partial fractions,
ie: combining terms to produce a quadratic in x.

A yes or no is what I am looking for.
If yes, I will attempt to work the problem.

We can also complete-the-square.

. . . . . . . . . . . .

. . . . . . . . . . . .

Then the left side has the form: .

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 Post subject: Re: separation of variables involving a quadraticPosted: Wed, 12 Sep 2012 01:57:25 UTC
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Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9633
Doesn't the derivation of that integration rule use partial fractions?

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 Post subject: Re: separation of variables involving a quadraticPosted: Wed, 12 Sep 2012 06:38:29 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
Matt wrote:
Doesn't the derivation of that integration rule use partial fractions?

I think so, but it's probably in some table as well, which is probably what Soroban surpressed.

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