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#26 2012-04-19 12:03:14
- bubokribuck
- Member
- Registered: 2011-10-28
- Posts: 42
Re: Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation.
Hi bobbym, thanks very much for that, I'll have a try myself 
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#27 2012-04-19 16:15:45
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation.
Hi bubokribuck;
See if you can get y(.2) on your own.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#28 2012-04-22 04:21:19
- bubokribuck
- Member
- Registered: 2011-10-28
- Posts: 42
Re: Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation.
Hi bobbym, I got y(0.2)=0.122826... , is it correct?
By the way, shouldn't p'=0.2y'(1-y^2)-y? The answers are slightly different this way, I got y(0.1)=0.109198 and y(0.2)=0.117486. Would you check it for me please. Thanks!
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#29 2012-04-22 05:21:40
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation.
Hi bubokribuck;
Very good you are correct about the missing y'! Please let me see your calculation of y(.1) and y(.2)
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#30 2012-04-22 06:58:28
- bubokribuck
- Member
- Registered: 2011-10-28
- Posts: 42
Re: Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation.
Hi, here's my calculations:
Also, how can I find the analytical solution for the problem please?
Last edited by bubokribuck (2012-04-22 07:00:34)
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#31 2012-04-22 07:06:41
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation.
Hi;
I would do this step last and not first
because you start with x0.
An analytical solution is unlikely. This DE has non linear terms y^2 and y'y.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#32 2012-04-22 10:39:46
- bubokribuck
- Member
- Registered: 2011-10-28
- Posts: 42
Re: Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation.
Hi, is there any analytical solution for the following problems please?
If there is any, how can I find it please?
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#33 2012-04-22 13:41:47
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Rewrite y''+0.2y'(1-y^2)+y=0 as 1st order differential equation.
Hi;
For the first one I had mathematica run it off:
is a solution.
The second one has non linear terms in it so again no analytical answer.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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