Path: news.mathworks.com!newsfeed-00.mathworks.com!kanaga.switch.ch!kasuga.switch.ch!news-zh.switch.ch!switch.ch!nrc-news.nrc.ca!newsflash.concordia.ca!canopus.cc.umanitoba.ca!not-for-mail From: Walter Roberson <roberson@hushmail.com> Newsgroups: comp.soft-sys.matlab Subject: Re: Diff Solution for D2(y) = 20*sin(y) - 200 Date: Tue, 23 Nov 2010 14:28:24 -0600 Organization: Canada Eat The Cookie Foundation Lines: 24 Message-ID: <ich85d$4ri$1@canopus.cc.umanitoba.ca> References: <icgpfs$r41$1@fred.mathworks.com> NNTP-Posting-Host: ibd-nat.ibd.nrc.ca Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: canopus.cc.umanitoba.ca 1290544109 4978 132.246.133.10 (23 Nov 2010 20:28:29 GMT) X-Complaints-To: abuse@cc.umanitoba.ca NNTP-Posting-Date: Tue, 23 Nov 2010 20:28:29 +0000 (UTC) User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.9.1.15) Gecko/20101027 Thunderbird/3.0.10 In-Reply-To: <icgpfs$r41$1@fred.mathworks.com> Xref: news.mathworks.com comp.soft-sys.matlab:689441 On 10-11-23 10:18 AM, amadeo constantine wrote: > I have problem on second order differential equation. > D2(y) = 20*sin(y) - 200 > > where D2(y) is second order diff of Y where Dy = dy/dt I try to use this: > Q = dsolve('D2y = -20*sin(y) - 200, 'y(0) = 0','Dy(0) = 0','t') > but it doesn't work because of sin(y). y(t) = RootOf( int(+/- 1/2/(10*cos(A)-100*A-10)^(1/2),A = 0 to Z) + t) That is, y(t) is the value Z such that t plus a certain integral from 0 to Z, becomes 0. The positive and negative of the integral are both solutions. The integral itself is independent of y and of t. The Maple command that I used for this was, dsolve({diff(y(t),t,t) = -20*sin(y(t)) - 200, y(0) = 0,D(y)(0) = 0}) ; Notice the change from sin(y) to sin(y(t)). The term (10*cos(A)-100*A-10)^(1/2) is imaginary for all positive A, so only negative A (and thus only negative Z) need be considered if you are looking for real solutions.