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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
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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.