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From: jablow@brahms.BERKELEY.EDU (Eric Robert Jablow)
Newsgroups: net.math
Subject: Re: value of an integral (differential equation)
Message-ID: <12087@ucbvax.BERKELEY.EDU>
Date: Thu, 27-Feb-86 21:20:58 EST
Article-I.D.: ucbvax.12087
Posted: Thu Feb 27 21:20:58 1986
Date-Received: Sat, 1-Mar-86 18:31:33 EST
References: <1396@decwrl.DEC.COM>
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: jablow@brahms.UUCP (Eric Robert Jablow)
Organization: Mathematical Sciences Research Institute
Lines: 48

In article <1396@decwrl.DEC.COM> moroney@jon.DEC (Mike Moroney) writes:
>
>Can anyone evaluate the following differential equation to the form
>y=f(x) (i.e. find f(x))
>
> " 2
>y y = K   y(0)=K  y'(0)=K
>                1        2
>
>K > 0
> 1
>
>(The " means second derivitive, ' means first derivitive, K, K , K  are
>fixed constants)                                              1   2
>
>Thanks in advance.
>
>-Mike Moroney
>
>..decwrl!dec-rhea!dec-jon!moroney

Standard trick: in any differential equation of the form

		f(y, y', y")=0		(no independent variable),

let p=y'.  Then y"=p'=p*(dp/dy) by the chain rule.  Thus you get

		f(y, p, p(dp/dy))=0.

This is a first order ODE in y.  Solve it to get

		g(y)=p=y'.

Solve this for y in the obvious fashion.

The **best** book on ODEs is Ordinary Differential Equations, by Ince.
Dover publishes it, so it is cheap.  It is old-fashioned, though.


			Respectfully,
			Eric Robert Jablow
			MSRI
			ucbvax!brahms!jablow

	I may be a screwy little wabbit, but at least I'm not
	going to Alcatraz!

				--E. Fudd--